US marines are pushing into areas not yet under their control
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US and Iraqi forces are continuing their assault against insurgents in the city of Falluja.
BBC correspondents in the region as well as in Washington and London bring you the latest updates on the attack. Where stated, some correspondents are embedded with US troops.
Jennifer Glasse:: EMBED at US marine HQ, Falluja :: 1824GMT
The top American and Iraqi generals in Falluja say they are pleased with the way the operation is progressing in the city.
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EMBEDDED REPORTERS
They can give general troop strength and casualty figures
They can report numbers of enemy POWs
They can give broad information about previous combat actions
Journalists cannot give specific details of locations
They cannot reveal the future plans of their unit
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US forces control at least two-thirds of Falluja and continue to fight their way through the centre of town.
Iraqi General Mohammed Djasem Abdukader said his forces found houses where he said kidnappers slaughtered their hostages.
Inside the building, Iraqi forces found lists of names, the black clothes worn by insurgents and weapons from a number of different countries.
American and Iraqi forces continue to move through Falluja searching houses, looking for insurgents or keys to their whereabouts.
Alastair Leithead:: Baghdad :: 1803GMT
While fighting has continued in Falluja there have been other outbreaks across Iraq, many of them thought to be a reaction to the battle.
On Wednesday, it was Mosul and Beiji in the north. A number of people are reported to have been killed in clashes between insurgents and US forces, Iraqi police and national guards.
And Ramadi, close to Falluja, has seen continued fighting, after insurgents took control of the city centre on Tuesday, and paraded guns and rocket launchers.
While the American-led forces may be pleased with the way their military action is going, the fallout from it is spreading across central Iraq.
Sunni Muslims are becoming alienated, and a popular and political victory still seems a long way away.
Jennifer Glasse:: EMBED at US marine HQ, Falluja :: 1710GMT
The top American marine officer in Falluja, Lt-Gen John Sattler, says insurgents are in small pockets moving throughout the city blind, and that US and Iraqi forces continue to hunt them down to destroy them.
Military officers on the ground have said they had expected the resistance to be more co-ordinated or better organised. Gen Sattler said he is confident that the tight cordon around the city is preventing any militants from escaping.
But American and Iraqi officials have said for weeks that military action was coming in Falluja - some insurgents may have left before the assault began on Monday night.
Gen Sattler said the mission in Falluja is the elimination of what he called terrorists and murderers, then to reinstate the rule of law and establish the conditions for reconstruction. He says there's still much work to be done.
Paul Adams:: BBC News Centre, London :: 1442GMT
The Americans seem poised to declare Operation Phantom Fury a success. Their progress through the streets of Falluja has been rapid, their own casualties relatively light. But how will we know if they have really succeeded?
Taking a city is one thing, but what happens when America's military attention is diverted to another city in the Sunni triangle? Will the militants, many of whom have slipped away well ahead of this week's assault, filter back, reclaiming Falluja once more as their stronghold?
This operation is part of a wider effort to set the stage for successful elections at the end of January. But for now Iraq's new leaders are seen by many as coalition puppets, a notion Operation Phantom Fury will not have dispelled.
It could be many weeks before the final verdict on this decisive battle is known.
Paul Wood :: EMBED with US marines inside Falluja :: 1300GMT
We moved on to a high-rise building and spent an hour and a half there, having initially gone to the roof because we spotted some Iraqis trying to surrender.
As soon as the translator stood up to take the surrender we came under heavy and sustained automatic and sniper fire from three different directions.
It took about an hour of calling in air strikes, of tanks coming to our support, to push the insurgents back.
We are now at the main road through Falluja. The battalion I'm with is pushing south of that main road. There are some 2km to go before Falluja is in US hands, but they do now have the centre, they do now have the north.
Paul Wood :: EMBED with US marines inside Falluja :: 1236GMT
A company of US marines entered the centre of Falluja just before dawn. They quickly gained a foothold in the city's abandoned police station. It was vital for them to establish a strong position by sunrise.
As soon as there was light, the attacks began from all sides. We were fired on by a sniper sitting in a minaret, just 100 metres away.
The marines then called in tanks. It fired at the mosque, destroying the dome. Falluja is known as the city of mosques, but this afternoon these holy sites are right at the heart of the battle.
The marines say they don't like to fire on mosques, but they have no choice when they're used by the militants to launch attacks.
American military sources are claiming to have killed hundreds of the insurgents so far. Some humanitarian aid has reached the hard pressed people of the city.
We don't know how many are still trapped here, but this afternoon the battle is still raging.
Quil Lawrence :: EMBED with US forces at Falluja :: 1215GMT
We have seen continued attacks not just here but in areas between Falluja and Ramadi. Convoys have been ambushed. One ambulance was hit by a car bomb.
In Falluja what's important is not a matter of the percentage they have taken, but how much they can control over the long term.
They need to provide a plan to turn the people away from the resistance and insurgents and make them believe their town will be rebuilt sooner if they co-operate with the interim government.
Talking to commanders they have no illusions about winning over the entire country with this one battle, but they could not leave a part of the country totally under the control of insurgents, for reasons of morale, and because Falluja allowed insurgents to openly set up bomb factories.
There have been at least 10 US deaths, and that's all I can confirm, and the Iraqi National Guard said two of their forces were killed. No-one has accounts of insurgent or civilian dead. It will be difficult to tell them apart.
Jennifer Glasse :: EMBED with US forces in Falluja :: 1110GMT
Commanders say things are progressing and they expect to control all of the city quite soon.
There are fights in the centre of the city itself. Insurgents have fired from at least two mosques, and troops don't want to go in there because of sensitivities. This makes things difficult for the US.
They are a disadvantage with this hard urban fighting because we see that when fired upon, the marines hit back with overwhelming fire power. And they don't want to destroy buildings, in order that people may come back to the city.
Jennifer Glasse :: EMBED with US forces in Falluja :: 1015GMT
The marines are fighting in the geographical centre and moving towards the south, where the forces are encountering sporadic insurgent fire. It's not as organised though as they thought it would be. We've heard fire supporting the US forces on the ground.
As far as civilian casualties go it's been eerily quiet, as was the case last April when they went into Falluja. It's difficult to get an independent observer on ground to verify the situation, but it's believed tens of thousands of people are still inside the city and we expect there are casualties.
The forces had dropped leaflets telling people to stay in their houses and not to get involved in the campaign.
It may be the leaders of the insurgents have slipped away and chosen not to make Falluja their last stand. There's talk that some have made it into Ramadi, or have decided to conduct a guerrilla war rather than stay here where they're outmanned and outgunned.
Jennifer Glasse :: EMBED with US forces in Falluja :: 0856GMT
US marines say American forces now hold seventy per cent of Falluja. They're battling through the centre of the city and have captured the main police station and the mayor's office.
As the offensive continues, American artillery and air power are backing up the forces on the ground. Insurgents are being pushed towards the southern end of the city. Falluja is surrounded, and a marine spokesman says the insurgents have nowhere to run.
The offensive has not been without cost. So far ten American troops and two Iraqi soldiers have been killed. There is political fallout as well.
The Sunni clerics association of Muslim scholars is calling for a boycott of elections in January, in protest of the American move into Falluja.
For the same reason, a main Sunni political party has withdrawn from the interim Iraqi government.
Caroline Hawley :: Baghdad :: 0825GMT
We are already seeing political fallout from Falluja. It's a controversial operation but there are many people who support it, because they believe something had to be done to stop what was happening there.
The abduction of Iyad Allawi's relatives seems to have been the closest insurgents could possibly have got to him. Allawi gets death threats every day and it's extremely difficult to get anywhere near him, such is his security.
A spokesman said he thought this could be some kind of revenge attack for Falluja.
Paul Wood :: EMBED with US forces in Falluja :: 0820GMT
We didn't get much opposition until shortly after dawn, when we got steady sniper fire coming in from the roof of the police station.
The marines have taken a foothold right in the centre and they're pushing through across the main road. There is now about 2km of the city not in marines' hands, but they are making steady progress, and according to one military source have killed hundreds of insurgents.
But they won't give any exact figure. There are a lot of insurgents out there. They are confident but are not setting out a timeline in any way.
We started to clear a small building, I think a school building. There was sniper fire and some Iraqis came out with a white flag. As soon as the forces stood up to indicate they wouldn't fire upon the people, we encountered very heavy fire coming at us from all positions.
There was then a very heavy battle which raged for about an hour and a half and this was pretty scary.
Claire Marshall :: Baghdad :: 0740GMT
The interim Iraqi prime minister's spokesman, George Sadr, has confirmed to the BBC that Iyad Allawi's cousin has been taken hostage. His cousin's wife was also kidnapped, along with another relative.
It's understood that an armed gang raided their Baghdad home. The timing of these kidnappings doesn't seem to be coincidence. It comes three days after Iyad Allawi ordered an assault on the rebel stronghold of Falluja.
For many people in Iraq, particularly the country's Sunni minority, this has been a controversial move. As one Baghdadi resident commented to the BBC earlier, how can brother strike brother? These kidnappings appear to be one militant group's form of retribution.
Paul Wood :: EMBED with US forces in Falluja :: 0528GMT
US marines are now right in the heart of Falluja, but have been waging a two-hour gun battle so far to gain control over it from the insurgents.
I'm with a company of the Marines 1-8. They have taken the police station and the mayor's offices in the centre of town. They moved in just before dawn without opposition.
First of all they blasted a hole in the outer wall of the compound using a tank, and then we took up positions on the roof of the police station.
Shortly after that we began taking sniper fire from a gunman apparently in the minaret of a mosque. We were pinned down for some time before a tank moved in on the mosque and also spotted a number of men with rocket-propelled grenades moving around the back of the mosque.
This mosque is about 100 metres from our position. The tank then fired a shell into the base of the mosque and we've been taking heavy small-arms fire since.
The marines have been replying with tank rounds - you just heard one there - with automatic fire. They have mortars and they may later call in an air strike.
So far, two marines have been very slightly injured - a rocket propelled grenade hit their armoured vehicle and one had concussion and one had a slight cut.
Otherwise the marines are okay. We're moving out now from the compound to try to clear the buildings around the mosque.
Jennifer Glasse :: EMBED with US forces near Falluja :: 0505GMT
Overnight we heard a lot less artillery fire. The operation has entered a sensitive stage: US forces want to take the city, but there has to be a city left to take.
There is a little bit of surprise that the insurgency is not as organised as they thought it would be.
TUESDAY
Nick Childs :: Pentagon :: 2002GMT
The number two US commander in Iraq, Lieutenant General Thomas Metz, has said that the operation in Falluja has achieved its objectives on or ahead of schedule in the first 48 hours.
"I think we're looking at several more days of tough urban fighting," said Gen Metz, the overall operational commander for the Falluja mission.
Iraqi government forces involved in the operation have performed admirably, as Gen Metz put it.
He described casualties on the US side as light - about a dozen, he said, but he wouldn't be more specific; and he said he believed there had been very few civilian casualties.
Insurgent casualties he described as significant but acknowledged that many of the leaders - including Abu Musab al-Zarqawi - had probably fled.
The insurgents are now fighting in small groups of three to six, he said, and without much coherence.
But according to him, the coming days will show whether US-led forces are pushing the enemy back, capturing or killing them, or whether the insurgents are just falling back.
Imogen Foulkes :: Geneva :: 1946GMT
Humanitarian organisations say they are deeply worried about the fate of civilians caught up in the fighting in Falluja.
Both the United Nations refugee agency (UNHCR) and the International Committee of the Red Cross expressed their concern and reminded the warring parties that civilians must be allowed access to food, water and medical care.
But since international aid agencies are no longer present in Iraq, it is extremely difficult for them to assess exactly how serious the situation is.
The UNHCR says tens of thousands of civilians have fled Falluja - no one really knows how many remain in the embattled city.
Aid workers are deeply frustrated that they can't help those in need; they are also concerned that the fighting is taking place without any independent humanitarian witnesses.
The Red Cross has called on the warring parties to take every possible precaution to spare civilians and has urged what it calls "distinction and proportionality" in military operations - a reminder that hospitals, schools and water and electricity supplies should not be targeted.
International agencies are trying to co-ordinate aid supplies with local organisations such as the Iraqi Red Crescent.
Jennifer Glasse :: EMBED with US forces near Falluja :: 1931GMT
US forces say they control at least a third of the city of Falluja a day after they launched a long-expected assault on the city.
So far, the American forces have captured three strategic objectives in the city.
Before entering Falluja, US Marines took the Falluja general hospital; they also control the main railway station on the edge of the city and a mosque they say insurgents were using as a meeting-point and a place to store weapons.
"Things have been changing - yesterday it was a timetable for the operations, and today everybody is optimistic about the way it goes, and we think it's going to end up in a very short time," the Iraqi interim prime minister's spokesman, Tahir al-Naqib, said.
The military operation to take Falluja may take a short time, but the test of its success will be whether it slows or halts the insurgency.
Caroline Hawley :: Baghdad :: 1737GMT
The assault on Falluja is meant to help pacify and prepare the country for nationwide elections.
But even before it began, there were fears and warnings from the UN that it could backfire.
Today an influential group of Sunni Muslim clerics is threatening to boycott the vote in protest at the offensive. The main Sunni political party has also announced it's withdrawing from the government.
Iraq is currently in a state of emergency. The interim prime minister, Iyad Allawi, has used his new powers to declare an indefinite night-time curfew here in the capital, Baghdad.
Paul Wood :: EMBED with US forces near Falluja :: 1714GMT
A tank commander who has just returned from inside the city had told me that the insurgents had now run out of armour-piercing grenades.
"Whenever we see them we just kill them," he said. "The problem is catching them."
This will be the problem in general when the joint American and Iraqi force is fully in possession of Falluja. It's the problem the coalition has always faced against the rebels.
The operation in Falluja is now entering a new phase. The battle for the heart of the city is about to begin. But no one believes that victory in Falluja will spell the end of the insurgency.
Quil Lawrence :: EMBED with US forces in Falluja :: 1707GMT
I'm at the main hospital in Falluja which was taken by Iraqi and US forces last night. We're now waiting to see if any casualties might come in for treatment.
But at the moment all of the roads and bridges out of the city are still closed so there would be no access if civilian casualties were to come through.
We've had a barrage of mortars and rockets and sniper fire all day. Night has just fallen and that gives the Americans a huge advantage because they have night vision equipment.
I haven't heard a shell come in for about half an hour. That's the longest period of silence we've had all day and I assume this is because the insurgents are now shooting blindly.
Nick Childs :: The Pentagon :: 1603GMT
Pentagon officials are giving few details about the fighting so far. Behind the scenes they say they believe the offensive is generally going according to plan.
Obviously there has been resistance, and one senior official said overall it has been less than expected so far.
But is that because the strategy has been working, because many of the insurgents have left or because the decisive battle has yet to be joined?
These are the questions the military planners are grappling with. Officials here acknowledge that many insurgents may have slipped away, but they still insist it'll be more difficult for them to regroup without Falluja.
Jennifer Glasse :: EMBED with US forces at Falluja :: 1515GMT
US officers here say things are going according to plan, that the plan is intact. Clearly people think things are going fairly well.
The military is very reluctant to talk about the injured or dead. One officer said: "This is not a numbers game. We knew there'd be a price to pay - we take the hits and move on."
At any time when there's fighting in an urban area it is difficult and there are casualties - but the US just doesn't know how high that price will be.
Quil Lawrence :: EMBED with US forces at Falluja :: 1505GMT
I can still see the battle unfolding across the river. The hospital where I am is just to the west of the city over the bridge.
You can see fierce fighting, though it has quietened down a little with the coming of darkness. The dark gives an advantage to the Americans because of their night vision equipment.
I imagine there must be many casualties considering the amount of gunfire I've seen. The Americans launch about 500 rounds to the insurgents' one, pelting the insurgent area - so I imagine the amount of casualties is high.
Alastair Leithead :: Baghdad :: 1356GMT
While intense fighting continues in Falluja, it seems a number of the insurgents that the US-led forces are so keen to confront have moved to a neighbouring city.
Ramadi - a city of a similar size to Falluja - has been another focal point for insurgency, and hundreds of guerrilla fighters armed with heavy machine-guns and rocket-launchers have taken up positions and control much of the centre.
There are reports that the American forces withdrew from Ramadi's main streets to their bases on the outskirts of the city.
Elsewhere in the Sunni Triangle, a number of police officers have reportedly been killed or injured in Baquba by another well-planned raid on police stations, and a suicide car bomb in Kirkuk is thought to have claimed three lives.
Paul Wood :: EMBED with US forces near Falluja :: 1310GMT
The trouble is the insurgents are now going to ground. So I think we can expect the territory of Falluja to be under joint American and Iraqi command in quite a short time, but after that the problem will be the wave of suicide bombings which American commanders expect to be unleashed.
The mopping up operation will be lengthy and will not be easy.
There is outgoing mortar fire from the company I am with. They are in that famous euphemism "softening up" the target before they go in.
There are two plumes of black smoke now rising up from the targets which they've been hitting.
Paul Wood :: EMBED with US forces near Falluja :: 1305GMT
The battalion I'm with has penetrated about a third of Falluja. There are parts of the city still to be reached so commanders expect this rapid pace to continue for a few more days.
The initial stages were about carving safe routes. Next troops will go down them - the battle for the heart of the city is yet to begin.
But with no independent reporters in Falluja it's hard to know the truth of what exactly the picture is there.
The US have killed the enemy wherever he has showed himself.
There are mortars going off right now behind me.
Falluja is only four kilometres across. Elements of the rest of the force have reached the centre but that doesn't mean they have it. The battalion I'm with have objectives there and this tempo will continue over the next 24 hours.
The guerrillas are doing what guerrillas do and are attempting to melt away. You will see the battlefield mutate and this isn't over by a long chalk.
Paul Wood :: EMBED with US forces at Falluja :: 1220GMT
The troops are in control of the northern third of the city - I haven't been able to verify that they have controlled the heart of the city. They may well have reached there.
Essentially phase one is over - but now the fighting has to begin at the very heart of the city and I expect the tempo of the operation to be maintained.
I can't tell you about civilian casualties but there have been some military casualties - they won't give us numbers but they are lighter than might be expected.
One commander said wherever they saw insurgents they took them out and went on to the next. The insurgents are being forced back into smaller and smaller areas - it's now out into the bigger streets of the centre and there is hard fighting ahead.
The battalion I'm with has an elite battalion of Iraqi troops - the Iraqis are right there on the front line. A mosque was seized this morning by the coalition but it was Iraqi troops who went into it. Where these government buildings are seized it's Iraqis who go in first and raise the flag.
Caroline Hawley :: Baghdad :: 1210GMT
I presume the curfew is being imposed by Iyad Allawi because of the current instability and the fear of further attacks. Allawi said Iraqi soldiers were going in to avenge victims of terrorist attacks, but there is a real fear that terrorists will take revenge for this assault.
One party called the Islamic Party, the main Sunni Muslim party in government, has withdrawn in protest at the operation in Falluja. A spokesman said this was the wrong approach, that violence would only beget violence.
There is a fear that this operation in Falluja will increase instability in the run up to elections.
It will be important to keep civilian casualties to a minimum. Tens of thousands have already left the city - we spoke to a resident who escaped to the outskirts this morning and spoke of a terrible situation there with bodies littering the streets in some areas and water and electricity being cut.
Sebastian Usher :: BBC Monitoring, Caversham :: 1205GMT
Many Arab papers dismiss the Iraqi government's justification for the assault on Falluja - that it was the only way to bring some security to Iraq.
Saudi Arabia's Al Watan says the real aim is for the Americans to impose their own order on the country in a way that will benefit Israeli political interests rather than the Iraqi people, and Al-Quds Al Arabi says the attack is just an excuse for the Americans to get even with and punish the Iraqis.
As one commentator says "God won't tolerate such an attack on innocent people."
Other papers criticise the interim Iraqi government for giving the go-ahead to the operation, saying that if it really wanted to build security, it would do so by improving humanitarian and political conditions in the country.
Jennifer Glasse :: EMBED with US forces in Falluja :: 1140GMT
We know the US marines have been moving street to street and are progressing quickly - commanders here are saying they control at least a third of the city. It would be no surprise if they were in the heart of the city as is being reported now.
It may be that they have just arrived in the centre - but arriving there and holding it definitively are two different things, especially here in a city like this which has been controlled by insurgents for so long.
The insurgents are outgunned but what they have on their side is the cover of the city. Marines say they are firing back and their fire is punishing.
Quil Lawrence :: EMBED with US forces in Falluja :: 1110GMT
I'm on the west bank with a combined marine and army unit. I can see a huge black cloud of smoke - the largest I've seen in the last two days. Marines are now approaching from the other side and are approaching a link up with those from this side.
I can hear small arms fire and today we're getting occasional sniper fire. Marines are responding disproportionately - they fire back with heavy machine guns.
Insurgents have one advantage, which is that they blend in with the population. I haven't seen any civilians today - yesterday I saw some waving white flags as they left.
Shortly after I saw one group leave, mortars came in close to their position. This demonstrates the bind the marines are in - they want to avoid civilian casualties but if they do nothing they are setting themselves up to be hit by insurgents dressed as civilians.
Quil Lawrence :: EMBED with US forces in Falluja :: 0935GMT
I'm just across the river on the west side of the city near the main hospital, seized by the US and Iraqis two nights ago. The marines are advancing and I can track their progress by the small arms fire. Black smoke is rising where buildings have been hit.
I've heard comments saying the operation is going a little quicker and is a little rougher than expected. I can't say how many numbers of insurgents the forces have met - but there were skirmishes this morning and they're taking sniper fire at the moment.
I heard some artillery a few minutes ago. At first I thought we were being shelled but it was shooting at an apartment.
The US soldiers have been gearing up for this for a long time. They seem almost excited to be getting there - some were preparing by listening to heavy metal music and one soldier told me it made it seem a bit more like a video game.
Jennifer Glasse :: EMBED with US forces at Falluja :: 0910GMT
I think the operation is going about as planned. The marines were expecting resistance and the insurgents have had months to prepare for this. This kind of fighting is always complicated.
The military is reluctant to talk about those killed or injured. We know 10 marines were injured in the early fighting, but the marines don't give out details because they don't want to help the insurgents to refine their attacks.
I don't think this will be an easy job but it's in the forces' best interests to get this over with. They don't want to alienate the population. However, they have been using homes as shelters and the only way they can do this is to use heavy weaponry, and this means destroying buildings.
But the people returning would like to have a city to return to and that's why this is such a tricky task.
It will be up to the insurgents what kind of battle they fight. This could be their last stand or they might continue to try to attack the forces wherever and whenever they can.
Jennifer Glasse :: EMBED with US forces at Falluja :: 0846GMT
The marines are trying to move forward into Falluja after a fierce night of fighting. They're moving street by street. In some cases, going house to house, looking for insurgents.
The US forces are trying to operate under their rules of engagement and are trying to avoid taking civilian lives.
It's a tricky situation because the fight is active and they will return punishing fire if they are being fired upon. This must be a very terrifying situation for civilians caught nearby.
The troops I'm with say the insurgents have been intimidating the inhabitants of Falluja for many months now there are claims that some civilians are being used as human shields.
Alastair Leithead :: Baghdad :: 0827GMT
The first shockwaves from the assault on Falluja have struck Baquba - another city in the Sunni triangle, where police stations have been targeted by guerrilla fighters.
US forces storm the main hospital in the city of Falluja
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There are reports of a number of police officers being killed or wounded by insurgents, attacking police stations with gunfire and rocket propelled grenades.
Also in Kirkuk, a suicide bomber blew up his car at a National Guard base in the city. There were some reported fatalities.
And here in Baghdad, the largest Sunni Muslim political party has withdrawn from the interim government in a protest against the attack on Falluja. The Iraqi Islamic party has pulled its minister of industry from the cabinet.
It's a symbolic move but one which will be a blow to the interim government as it tries to encourage as many groups as possible to take part in the elections planned for January.
Paul Wood :: EMBED with US forces near Falluja :: 0814GMT
It's already apparent that marines are having to fight every step of the way into Falluja.
The battalion I'm with went in to the city 12 hours ago and has managed to get a kilometre into the city. That shows every street, almost every house, is being contested.
What they're facing is insurgents darting out, firing at them and a lot of artillery has been called in to support their efforts.
The drive is still going on now. Twelve hours after the initial first wave went in, there is still the sound of heavy fire emanating from Falluja.
It's believed that dozens, if not more than 100 insurgents have been killed. Meanwhile the marines say they have reached one of their first objectives - the largest mosque in Falluja.
They say this is used as a meeting place for leaders of the insurgency. They claim it is heavily fortified and an arms cache and that people who work with the coalition, and are caught by the insurgents, are taken there and killed.
They're now wondering if they'll find bodies when they go in.
Paul Wood :: EMBED with US forces near Falluja :: 0528GMT
More than 12 hours after the assault began, the sounds of battle are still constant from Falluja.
Overnight the battalion I'm with, the 1-8, took its first serious casualties as the marines advanced street by street, clearing out gangs of insurgents armed with rocket propelled grenades.
Companies from the 1-8 have now advanced one kilometre into Falluja. They are now at the al-Hyderi mosque and are preparing to storm it along with Iraqi troops who will actually take possession of this sensitive site.
The marines' intelligence officer said the al-Hyderi mosque - one of the biggest in Falluja - was used as a meeting place for leaders of the insurgency and had both weapons and armed men inside
The marines also believe that Iraqis suspected of working with the coalition are taken to al-Hyderi, tortured and killed.
Quil Lawrence :: EMBED with US forces near Falluja :: 0510GMT
I am standing on the top of a bombed-out building just across the river, maybe 200 or 300 metres from Falluja.
Right now I am seeing extremely intense fire fights within the city.
We've seen helicopter gunships swooping in and firing missiles at targets.
At the moment we are receiving very little fire from across the river to this position.
At the moment it seems that the insurgents within the city have been distracted by a different force.
MONDAY
Paul Wood :: EMBED with US forces near Falluja :: 2205GMT
There are still steady explosions coming from the city, but the intensity of the battle in the early evening has eased slightly.
I am still watching tracer fire going into the city.
But the initial force that has pushed in has now managed to enter, and from the sound of the explosions, seems to have got some way into Falluja.
It has been an evening of heavy air strikes, an evening of tanks rumbling about and several huge explosions, some of which are devices to detonate roadside bombs, and some of which are weapons caches being detonated.
There has been opposition. Several artillery strikes have been called in to deal with roaming groups of men firing rocket-propelled grenades at the tanks.
But that opposition appears to be easing.
One marine officer said to me that their operation is very much on schedule.
Jennifer Glasse :: EMBED with US forces at Falluja :: 2051GMT
US officials say they will not stop until their forces control all of Falluja.
The main thrust of the initial assault on Falluja came from the north of the city, where US and Iraqi forces took the main railway station.
The long-expected offensive then followed from all sides as thousands of American troops, some with Iraqi forces at their sides, moved into Falluja.
US marines and soldiers are inside several parts of the city and are advancing.
Along the way they have encountered explosive booby traps along the roads set by insurgents who have had months to plan for this offensive. US forces were using explosives to detonate the traps.
As forces advanced, Falluja was dark. The sound of artillery, gunfire and US planes overhead punctuated that night-time scene.
US tanks and ground forces are working to move further into the city. They have cut off all roads in and out of Falluja to prevent any insurgents from leaving.
Nick Childs :: The Pentagon :: 1915GMT
The top US commander in Iraq, General George Casey, has said he expects the battle to retake the insurgents' stronghold of Falluja will be tough.
Speaking by telephone to Pentagon reporters from his headquarters in Baghdad, he said it involved some 10-15,000 US and Iraqi forces with the Americans providing the majority of the forces.
General Casey said mission was codenamed al-Fajr, or dawn - a name which, he said, had been chosen by the Iraqi interim Prime Minister, Iyad Allawi.
He acknowledged that the fight for Falluja would be a tough one and that there would be other tough fights to follow and while he believed that some of the insurgents may have slipped away, he said others have moved in.
He said he expected them probably to fall back to the centre of the city where there could be what he described as a major confrontation.
General Casey also said he believed some 50-70% of the civilian population had also left the city, although that could still mean perhaps 100,000 remain.
Paul Adams :: BBC News Centre, London :: 1742GMT
We know that a large number of civilians have left the city. Its population is between 250,000 and 300,000 people. The Americans are suggesting that 80 or 90 percent of the population may have left. But it also suits them to say that.
If that is the case, it will make the job that much easier. If they find themselves in a more or less deserted city the battle against the 3,000 to 5,000 militants would make the operation much quicker.
They will want to carry out the operation as quickly as they can and to create as little "collateral damage" as possible. The whole point of this is to deliver the people of Falluja to the elections in January.
Nick Childs :: The Pentagon :: 1719GMT
I don't think anyone is under any illusions there are risks involved in the assault and that the assault on Falluja is a very risky undertaking.
But it is also a balance of risks and the political risks of doing it, the Americans and Mr Allawi feel, are outweighed by the risks of not doing it.
Clearly it was critical that Mr Allawi gave the green light publicly. Part of the strategy is that this is seen to be with the blessing of the interim Iraqi government and crucially Iraqi forces will be taking part.
The great concern here at the Pentagon is that they can win a military victory but lose the political battle because of the images of the assault and potentially high casualties.
Paul Wood :: EMBED with US forces near Falluja :: 1712GMT
The Americans are going in with both infantry and marine rifle companies supported by tanks, and with air power used to a very heavy extent.
We just felt a shock wave through us as what we believe was a few thousand pound bomb was dropped on targets on the perimeter of the city.
We're getting chat coming back over the radio that there is resistance. Put simply, when it shows itself they blow it away it's a simple as that.
The US are going in with overwhelming force. They are going in very quickly. They are going in with assets that the insurgents can't command.
But they do have a healthy respect for their opposition. The company commander here called them "plenty mean and plenty tough".
But he added that they were about to encounter a level of violence they couldn't imagine.