US forces and Iraqi militants have been engaged in heavy fighting on the eastern edge of the city of Falluja.
US troops are maintaining a blockade around the city
US tanks and aircraft pounded insurgent positions and the rebels responded with mortars and rocket-propelled grenades, according to witnesses.
The troops have now pulled back but are maintaining a blockade around the city.
Iraq's most wanted man, Abu Musab al-Zarqawi, has reportedly pledged allegiance to al-Qaeda's leader in a message posted on an Islamic website.
In an as yet unverified message, Zarqawi appeared to call for unity with Osama Bin Laden against the "enemies of Islam", saying contact with al-Qaeda had been resumed after an eight-month gap.
US forces pulled back at sunset on Sunday.
Marines said in a statement late in the day that they had used small arms, tanks, artillery and mortars, and made seven precision air strikes against insurgents.
The rebels were seen taking refuge in a mosque, the statement said.
One witness spoke of direct clashes in the north-eastern neighbourhood of Jolan, an area said to be favoured by gunmen.
AFP news agency quoted him as saying he had heard US loudspeakers saying: "Come out and face us you cowards."
The military operation is seen as a crucial part of an offensive intended to regain control of rebel-controlled areas ahead of elections planned for January.
In other developments:
Nine Iraqi policemen die late on Saturday in an ambush near Latifiya, south of Baghdad, as they are returning to Karbala from a training course in Jordan
- At least two people are killed in a mortar attack on an arms collection point in Baghdad's Sadr City slum, on the last day of a weapons handover by Shia
A Jordanian prosecutor brings new charges against Zarqawi and 12 others including conspiring to commit terror attacks in Jordan
Two US soldiers are killed and two injured as two US helicopters crash south-west of Baghdad late on Saturday.
Falluja has been surrounded since Thursday. American bombers have been attacking targets there almost on a daily basis.
Residents reported air and artillery bombardment with explosions booming across the city on Sunday morning.
Smoke rose from the eastern Askari region and the southern area of Shuhada.
Many homes on the outskirts of Falluja have over the past few weeks been abandoned by their owners.
More fled Sunday's fighting, according to the Associated Press news agency.
US air strikes killed three people in the city overnight on Saturday, hospital sources said.
Efforts to find a peaceful solution broke down last week when the interim Iraqi government insisted that Zarqawi be handed over.
Representatives from the town said this was an impossible demand since they did not know where he was.
But local leaders have now made clear they are keen to resume talks to try to stave off an all-out assault, says the BBC's Caroline Hawley in Baghdad.
They are first demanding an end to the air strikes and the release of the main negotiator who was detained two days ago.