Lieutenant General Thomas Metz said about a dozen US troops have been killed in a two-day-old assault on the city. Refusing to provide specifics, Metz said there have been "very few" civilian, and larger than expected insurgent casualties.

"I think we're looking at several more days of tough urban fighting," he told reporters in a video teleconference from Iraq.

US forces easily penetrated the insurgents' outer defenses, however, and were now opposed by small, poorly organized groups of fighters, Metz said.

The general said he assumed that Zarqawi, the militant blamed for spectacular car bombings, kidnappings and beheadings that have rocked Iraq for months, was no longer in Fallujah.

US forces still have intelligence capabilities in the city dedicated to finding him, but the hunt for the Jordanian stretches across the country, Metz said.

US forces did not clamp a tight seal on the city until two days ago, Metz said, allowing insurgents to enter or leave the city.

"I personally believe some of the senior leaders probably have fled," he said. "I hope not, but I have to assume those kind of leaders understand the combat power we can bring and the fact that we will free Fallujah of anti-Iraqi forces."

The coming days will tell whether the insurgent force is "thickening as he moves back into the city, or we are killing the enemy or capturing enemy or pushing the enemy back," he said.

"I am very pleased at the position that we have the force in right now and the situation that the enemy is facing. He doesn't have an escape route because we do have the cordon around the city very tight."

As US forces assaulted Fallujah, insurgents mounted attacks in Baquba, Ramadi and Mosul.

Metz said the attacks in the so-called Sunni triangle were expected and that US forces had prepared rapid reaction forces ahead of the assault to deal with them.

But asked about the massacre of Iraqi police in Baquba, he said, "Obviously, we regret that particular success by the enemy."

"I think because Fallujah has been the cancer, that when the cancer is removed it will impact other places, especially Ramadi, especially Baghdad and other parts of the triangle that you mentioned," he said.

The battle for Fallujah has unfolded about as US commanders expected from pre-assault war games, said Metz, who estimated the number of insurgents in the city at between 2,000 to 3,000.

"We felt like the enemy would form an outer crust in the defense of Fallujah. We broke through that pretty quickly and easily," he said.

"We also then anticipated him breaking up into small, three- to six-person detachments or squads, which we've seen throughout the day today especially," he said.

US forces were using electronic jamming to disrupt communication among insurgent groups, he said.

Fewer bombs and booby-traps have been encountered than expected, and a curfew imposed by the government has made it difficult for insurgents to use car bombs, he said.

Few insurgents have been captured in the fighting, he said.

"I think the enemy is fighting hard, but not to the death. And I think that they are continuing to fall back," he said.

"In many cases, it's hard to tell whether or not the enemy was killed in a particular engagement because of the complexity of urban terrain," he said.

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