US-led coalition forces have exchanged heavy fire with insurgents in Falluja as they prepare for a major offensive.
Troops seized control of a hospital in the west of the city
Witnesses reported black smoke rising from several locations as US forces unleashed a fierce artillery barrage.
Meanwhile fighters in the city fired mortars and small arms across the River Euphrates at American positions.
US troops, who are massed near the city awaiting orders for an attack, took two bridges and a hospital overnight in the western part of the city.
But they have not entered deep into the city, and have repeatedly had to change position due to the insurgents' fire.
The Associated Press news agency reported that US marines died overnight when their bulldozer overturned in the river. Their bodies were discovered in the morning.
Groups of civilians waving white flags were seen leaving the outskirts of the city.
American troops let them pass, but coalition forces suspect some insurgents may be posing as civilians - soon after a pair of unarmed men approached a group of army engineers, rockets landed within 20 metres of the soldiers.
State of emergency
The BBC's Quil Lawrence, with US forces near Falluja, said troops used night vision to seize the two bridges, which are main routes west out of the city.
One of the bridges was the site of the killing of four US contractors that sparked the first attempt to retake Falluja in April.
There is no sign yet of American ground forces entering the city centre, where street by street fighting is expected, our correspondent adds.
US planes and artillery have been battering what they call insurgent positions for the past few weeks to make entry into the city easier.
On Sunday, Mr Allawi declared a 60-day state of emergency across the country.
The move was a response to the escalation of violence by militants, said official spokesman Thaer Naqib.
More than 60 people have died in two days of co-ordinated attacks by insurgents in an apparent response to US military preparations around Falluja.
Late on Sunday, correspondents embedded with the US marines outside Falluja said military action seemed imminent.
The BBC's Paul Wood says the marines believe Falluja will be their biggest engagement since Hue, the Vietnamese city they captured in 1968, losing 142 men and killing thousands of the enemy.
There are fears that insurgents will unleash suicide attacks on the troops once they have entered Falluja, our correspondent says.
On Sunday, insurgents stormed a police station in the western province of al-Anbar, disarmed 21 officers and shot them dead.
Fighting at the Haditha police station, 200km (120 miles) west of Baghdad, lasted about 90 minutes, sources said, as the building was attacked with rocket-propelled grenades and mortars.