But Sheik Abdul-Sattar Edatha, the spokesman for the shura council, said most foreign fighters had already left the city. The U.S. military had estimated that there were 2,000 to 3,000 foreign fighters in the city, many of them part of a network linked to Jordanian-born guerrilla leader Abu Musab Zarqawi.
"Militarily speaking, the city falls under the U.S. forces' control," Edatha said. "The foreign fighters won't stay here and die. They lost the battle. They spread in other places."
Marines from Charlie Company of the 1st Battalion, 8th Regiment take up positions along a narrow street in Fallujah.
(Luis Sinco -- Los Angeles Times)
A view of the city of Fallujah from the IKONOS satellite.
AP Video Report: Bush Visits Wounded Troops
Map: U.S. military commanders said their advance from the north was intended to surprise the insurgents.
Photo Gallery: U.S. forces began a long-anticipated urban offensive on the Sunni stronghold of Fallujah.
On Tuesday night, Fallujah's eerily empty streets were littered with shattered concrete and dead bodies, said a resident shaken by a missile strike on the second story of his family home. Insurgents cloaked in checkered head scarves carried wounded fellow fighters to mosques.
Civilians caught in the crossfire were gathered in a hospital donated by the United Arab Emirates and flying a blue and white UNICEF banner. There, medical workers low on bandages and antiseptic bound wounds in ripped sheets and cleaned torn skin with hot water.
The Jolan and Askali neighborhoods seemed particularly hard hit, with more than half of the houses destroyed. Dead bodies were scattered on the streets and narrow alleys of Jolan, one of Fallujah's oldest neighborhoods. Blood and flesh were splattered on the walls of some of the houses, witnesses said, and the streets were full of holes.
Some of the heaviest damage apparently was incurred Monday night from air and artillery attacks that coincided with the entry of ground troops into the city. U.S. warplanes dropped eight 2,000-pound bombs on the city overnight, and artillery boomed throughout the night and into the morning.
"Usually we keep the gloves on," said Army Capt. Erik Krivda, of Gaithersburg, the senior officer in charge of the 1st Infantry Division's Task Force 2-2 tactical operations command center. "For this operation, we took the gloves off."
Some artillery guns fired white phosphorous rounds that create a screen of fire that cannot be extinguished with water. Insurgents reported being attacked with a substance that melted their skin, a reaction consistent with white phosphorous burns.
Kamal Hadeethi, a physician at a regional hospital, said, "The corpses of the mujaheddin which we received were burned, and some corpses were melted."
In addition to ripping open entire neighborhoods, the armor assault also brought into the open an insurgent command that until this week remained shadowy even to Fallujah residents. Ex-generals from the former Iraqi army's Republican Guard passed written orders, complete with official stamp, to subordinates who snapped salutes, witnesses said.
Iraq's new army, formed after occupation authorities dismantled the armed forces that had served during the rule of Saddam Hussein, is taking part in the fight against insurgents in Fallujah, primarily as a rear element to help clear areas once U.S. forces have moved through. Marine commanders have declined to comment on the offensive, deferring to Iraqi officers. On Tuesday, Brig. Gen. Abdul-Qadir Muhammed Jasim characterized the offensive as "a holy task to fight for Fallujah people."
"We will fight to the last drop of our blood to free our people," he said at a news conference just outside the city. "We will fulfill the tasks we've been asked to do, with the cooperation of our friends."
Jasim said that resistance had been lighter than expected and that the Iraqi soldiers were in good spirits and eager to finish the operation.
"The operation is going very precise and with a very small number of casualties," he said. "In every place we finish an operation, our forces start to distribute aid, food, clothes, blankets and even money. . . . We are very sure that we are moving in the right way and will do the tasks we are asked to do very precisely."
Metz repeatedly praised Iraqi forces, saying they had "acquitted themselves very well in this fight." Metz said the Iraqi soldiers had been used especially to search the city's 77 mosques. "In several mosques today, lots of munitions and weapons were found, and they were found by those Iraqi soldiers," he said.
Metz's account suggested a marked improvement among the Iraqi troops in recent months. In April, the last time U.S. commanders tried to use Iraqi forces in Fallujah, a battalion of freshly trained Iraqi troops refused to go.
A senior Iraqi official said it was too early to tell how the Iraqi forces performed. "During the operation you always hear they're doing good," said Industry Minister Hachim Hasani. "After the operations are finished, we'll find out."
Hasani's political organization, the Iraqi Islamic Party, quit the interim government Tuesday to protest the Fallujah offensive. But Hasani, who opposed the U.S. Marine siege of the city earlier this year, quit the party Tuesday and retained his cabinet post. "Iraq is larger than any party," Hasani said. "Things should be done through the government, not outside the government."
Vick and special correspondent Bassam Sebti reported from Baghdad.