The top U.S. commander in Iraq (search) on Monday predicted a "major confrontation" on the streets of Fallujah (search) as a U.S.-led force of as many 15,000 troops pressed to retake control of the Sunni Muslim city.

Gen. George Casey said that the offensive, which began on Sunday, was proceeding on schedule and that he expected the insurgents to use homemade roadside bombs and car bombs as their "weapon of choice."

With as many as 15,000 troops participating in the siege, he predicted that insurgent defenders on the outer edges of the city would fall back into the city center for a "major confrontation" with U.S. and allied Iraqi forces.

As the fighting raged in Iraq, Casey said in a conference call with reporters at the Pentagon that the 50 to 70 percent of the city's roughly 200,000 people had left, meaning there could be as many as 100,000 people still there. Some insurgents managed to slip away, he said, while others "have moved in."

Casey was asked if he had enough troops for the operation.

"We absolutely do," he said. "If I came across a situation where I needed more troops, I will ask for them."

Casey described the Iraqi rebels as "an amorphous group of terrorists and insurgents" and said not one single group appeared to be in change.

"The Iraqi people are fighting to throw off the mantle of terror and intimidation so that they can elect their own government and get on with building a better life for all Iraqis," he said. "The elimination of Fallujah as a terrorist safe haven will go a long way toward those goals."

Casey said U.S. troops had secured a hospital used as a staging area by Sunni insurgents and two bridges across the Euphrates River (search). One of the bridges was where Iraqis hung the charred bodies of at least two of four American contractors last March.

Both the bridges and the hospital are on a peninsula.

"We went in and did it very quickly," Casey said.

He refused to give a specific count or breakdown of the U.S. and Iraqi forces involved in the operation, but said 10,000 to 15,000 was "in the ballpark."

Casey said there were "a good number of Iraqi battalions involved in this operation." He said that more battalions would be involved in the fighting in Fallujah than the two battalions involved in Najaf last summer and the five used in recent fighting in Samarra.

Casey predicted that insurgent fighters now positioned on the outskirts of the city "will probably fall back toward the center of the city, where there will probably be a major confrontation."

Forces from Britain's Black Watch battalion were participating, working along the west bank of the Euphrates River to disrupt any insurgent movement between Baghdad and Fallujah, Casey said.