US forces say they have taken control of part of the Iraqi town of Fallujah after several hours of heavy fighting.
Falluja is completely sealed off
Hundreds of marines backed by tanks, helicopter gunships are involved in the operation against Iraqi insurgents.
US Defence Secretary Donald Rumsfeld said troops had captured a number of people and killed others who resisted.
He promised a "methodical effort" to find those responsible for killing and mutilating four US security guards in the Sunni-dominated town last week.
US forces have sealed off Fallujah, which has been a focus of resistance to the US-led occupation of Iraq.
A night-time curfew has been imposed in the town, which the US has vowed to "pacify".
A US military spokesman said the marines had taken control of the industrial area on the town's southeastern outskirts.
28 April 2003: US paratroopers shoot dead 13 demonstrators
May 2003: Grenade and gun attacks on US troops become a routine occurrence
November 2003-January 2004: Three helicopters are shot down in the area with the total loss of 25 lives
31 March 2004: Four US security guards killed and mutilated
Witnesses spoke of explosions and gunfire echoing across the town as troops clashed with local gunmen.
About 1,200 US troops as well as Iraqi security forces began the offensive in Falluja on Monday.
The main road through the region which links Baghdad and Jordan has been closed.
Four US troops died in Anbar province on Monday, but the military did not say whether they were killed in Falluja.
Four members of the 1st Marine Expeditionary Force were killed on Monday while "conducting security and stabilisation operations", the US military said in a statement.
It did not give any details but said the deaths came "as a result of enemy action" in western Anbar province.