Thousands of U.S. and Iraqi troops have pushed into Fallujah in a long-awaited assault to retake the city from insurgents.
The troops, backed by airstrikes, tanks and artillery, faced resistance as they moved in.
Iraq's interim Prime Minister Iyad Allawi visited Iraqi troops hours before the assault. He vowed to restore the rule of law to the city.
In Washington, U.S. Defense Secretary Donald Rumsfeld said he does not think there will be large numbers of civilian casualties during the fight for Fallujah. U.S. officials say at least one half of the city's residents evacuated before the attack, which would leave up to 100,000 people remaining.
The officials say 42 insurgents have been killed so far. Two U.S. Marines died when their bulldozer flipped into the Euphrates river.