The commander of the US-led air campaign in Iraq says Republican Guard units outside the capital Baghdad are "dead", following intense bombardment.
US troops entered Baghdad for the first time on Saturday
Constant air patrols are now possible over the capital unhindered by Iraqi defences and coalition tanks made forays across the city limits for the first time on Saturday, US officials said.
Iraqi authorities however said they had repulsed an American attack from the south, claiming: "We were able to chop off their rotten heads."
Iraqi tanks and heavy armour were deployed in Baghdad for the first time since the war began but there was defiance from the leadership.
State television read a statement from Saddam Hussein and then broadcast pictures of him and both sons at a military meeting, though the date and authenticity could not be established independently.
The intensity of bombing increased again with the fall of darkness with loud explosions reported in the centre of Baghdad and to the south-west, towards the international airport seized by US forces.
But Andrew Gilligan, a BBC correspondent in Baghdad whose activities are restricted by authorities, says it was no worse than previous nights.
The US air commander, Lieutenant-General Michael Moseley said bombing raids had begun to wane, having achieved many of their objectives.
"The Iraqi military as an organised defence in large combat formations doesn't really exist anymore," he said.
There were still Republican Guard soldiers around, he conceded, saying: "We haven't killed all of them but the ones that are still around are walking with a bit of a limp."
General Moseley added: "The equipment is there and some of the people are there, but as far as corps and division strength, bringing to bear that combat power on the coalition, it's not the same as it was a couple of weeks ago."
US military officials said 25 Abrams tanks and 12 Bradley armoured vehicles had entered Baghdad's Dawra suburb on a tour from the airport during daylight hours.
The convoy met some resistance and returned to the airport, but achieved its goal, according to US Major-General Victor Renuart.
"The message... is to in a way put a bit of an exclamation point on the fact that coalition troops are in the vicinity of Baghdad... and demonstrate to the Iraqi leadership that they do not have control," he said.
"It was very clear to the people of Baghdad that coalition forces were in the city. That image is important," he said.
But western journalists, including BBC crews, who fanned out across the city of five million people later found no sign of US forces.
They said it the regime was obviously still in control of Baghdad, with members of Fedayeen militia driving around firing weapons into the air.
Power has been restored to much of the city after two nights of blackouts but groups of civilians have been seen leaving and cars carrying families and their belongings are reported heading to the Iranian border.
The Red Cross says several hundred civilians have been admitted to hospital with war-related injuries in the last few days.
In other developments:
- Sheikh Muhammad Sayyed Tantawi, the grand imam of Egypt's al-Azhar Mosque seen as the highest spiritual authority for Sunni Muslims, says Saddam Hussein was wrong not to go into exile to avert the US-led war
- US army officers say units have captured the headquarters of the Republican Guard's Medina Division south of Baghdad
HAVE YOUR SAY
This battle will be won by America and its allies at a great cost to innocent Iraqi people
Mohammad Shoaib, Delhi, India
- American B-52 bombers attack Iraqi positions about 10 kilometres from the northern city of Mosul
- US rangers and special forces are reported to have taken control of the road leading to Tikrit - the ancestral home and stronghold of the Iraqi president
- UK forces are sending forensic specialists to a site near the southern city of Basra where as many as 200 coffin-sized boxes containing human remains were found.