Small bands of gunmen - fewer than 20 - were engaging U.S. troops, then falling back in the face of overwhelming fire from American tanks, 20mm cannons and heavy machine guns, said Time magazine reporter Michael Ware, embedded with troops. Ware reported that there appeared to be no civilians in the area he was in.
On one thoroughfare in the city, U.S. troops traded fire with gunmen holed up in a row of houses about 100 yards away. An American gunner on an armored vehicle let loose with his machine gun, grinding the upper part of a small building to rubble.
Elsewhere, witnesses reported seeing at least two American tanks engulfed in flames. A Kiowa helicopter flying over southeast Fallujah took groundfire, injuring the pilot, but he managed to return to the U.S. base.
A major first objective was a mosque about a half-mile in from the city's northern edge that the military said was being used as an arms depot. U.S. troops surrounded the site while Iraqi forces entered the mosque, the BBC reported.
Iraqi troops seized several mosques in the city and uncovered weapons caches, Metz said. "Iraq forces are leading the attack through culturally sensitive areas," Maj. Gen. Abdul Qader Mohan, appointed by Allawi to lead Iraqi forces in Fallujah, said. "Areas with schools, hospitals and mosques (will be) under the operational control of the Iraqi army."
Troops searched houses for gunmen and weapons, dashing across the mouths of the narrow alleys to avoid the line of fire. A psychological operations unit blared Arabic announcements meant to goad gunmen out onto the streets. "Brave terrorists, I am waiting here for the brave terrorists. Come and kill us. Plant small bombs on roadsides."
Metz told reporters that he was working "on the assumption" that Abu Musab al-Zarqawi - the most wanted terror leader in Iraq - had left Fallujah. But he insisted those fighters still in the city don't "have an escape route. We have the cordon around the city very tight."
U.S. officers said few civilians were trying to flee the city Tuesday. They said the bulk of the population of 200,000-300,000 left before the fighting and the rest were hunkered down because of a 24-hour curfew. U.S. troops were preventing most people from leaving, except in emergency cases. One funeral procession was allowed out of the city, U.S. officers said.
U.S. forces cut off electricity to the city. Residents said they were without running water and were worried about food shortages because most shops in the city have been closed for the past two days.
"The north of the city is in flames. I can also see fire and smoke ... Fallujah has become like hell," Fadril al-Badrani, a resident in the center of Fallujah, said Monday night amid a heavy air and artillery barrage. He said hundreds of houses had been destroyed.
Some 10,000-15,000 U.S. troops have surrounded Fallujah, along with allied Iraqi forces, according to the top U.S. commander in Iraq, Gen. George Casey. Commanders estimate around 3,000 Sunni fighters are in Fallujah, perhaps around 20 percent of them foreign Islamic militants.
So far, the military has only confirmed five deaths and 14 wounded in Fallujah: three troops killed Tuesday, and two Marines who died in a bulldozer accident Monday.
The question of Iraqi civilian casualties is a major factor in the offensive. Reports of hundreds of people killed during the Marine offensive in April outraged Iraqis and forced the Marines to pull back - allowing guerrillas to strengthen their hold on the city.
The assault risks alienating Iraqis - particularly among the Sunni Arab minority. The mainly Sunni Iraqi Islamic Party quit the government Tuesday in protest, firing its one member on the Cabinet - Industry Minister Hajim Al-Hassani - when he refused its demands he resign.
Arab League Secretary-General Amr Moussa said he hoped the violence "ends fast," adding that he was in touch with Iraqi officials. "No one can ever accept the way civilians are struck in Fallujah," he told reporters.
The U.N. refugee agency said Tuesday that it was "extremely concerned" about tens of thousands of people who fled ahead of the Fallujah fighting - many of them now living in tents. And the International Committee of the Red cross said it received reports of some wounded Iraqis unable to get care because of the fighting.
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Contributing to this report were Associated Press correspondents Robert Burns in Washington; Edward Harris in Fallujah; and Tini Tran, Mariam Fam, Katarina Kratovac and Maggie Michael in Baghdad.
