U.S., Iraqis enter Falluja's center
Pentagon says 10 U.S., 2 Iraqi troops killed
Smoke billows from Falluja as U.S. soldiers and Marines pound the city Tuesday with airstrikes and artillery.
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Watch for CNN correspondents' frequent updates on the situation on the ground: live reports from the U.S.-Iraqi offensive in Falluja.
U.S. forces continue assault on eastern outskirts of Falluja.
Falluja insurgents have had months to prepare.
FALLUJA, Iraq (CNN) -- U.S. and Iraqi troops reached the heart of Falluja on Tuesday as the second day of battles continued in the insurgent-controlled city west of Baghdad.
The Pentagon reported that 10 U.S. troops and two Iraqi soldiers had been killed in the fighting, along with 22 others wounded, as of 10:30 a.m. Tuesday ET.
"So far, we have achieved our objectives on or ahead of schedule," Lt. Gen. Thomas Metz told reporters from Iraq. He described the number of coalition and Iraq casualties as "light," but said insurgent casualties appear "significantly higher than I expected."
Military sources said they were unsure whether they had intercepted the core of the insurgency.
"I think we're looking at several more days of tough urban fighting," Metz said. "The fight for Falluja is far from over."
Nevertheless, U.S. and Iraqi forces have faced less resistance than expected, said Lt. Col. Pete Newell with Task Force 2-2 of the Army's 1st Infantry Division.
Soldiers said they have dodged sniper fire and destroyed booby-traps, but not as many as anticipated.
Insurgent casualty numbers have mounted. Newell said his unit has killed or wounded 85 to 90 insurgents.
The insurgents' outer forces have been destroyed, Metz said, and they are fighting in small groups "without much coherence," using rocket-propelled grenades and small arms.
Only a few of the insurgents in the city have been captured, he said.
Insurgents may have slipped away
Falluja is considered an insurgent command-and-control center for the rest of the country and a base for Jordanian militant Abu Musab al-Zarqawi's terror network. (Map of Falluja)
Military officials have said 3,000 to 5,000 insurgents may have been inside the city, but they acknowledge many may have slipped away amid widespread reports of a planned offensive.
"I personally believe that some of the senior leaders probably have fled," Metz said.
Asked about the possible whereabouts of al-Zarqawi, he said, "I think it would be fair to assume that he has left."
Michael Ware, Time magazine's Baghdad bureau chief, who is embedded with Army Task Force 2-2, said his group encountered sporadic resistance from small groups of insurgents, with the most being 25 in one place.
CNN Baghdad bureau chief Jane Arraf, embedded with the same Army unit, watched from an armored vehicle as a firefight broke out.
Arraf described buildings crumbling from explosions and sheet metal flying like paper but said no insurgents were in sight.
U.S. Central Command described as "unsubstantiated" a report by the Arabic-language news organization Al-Jazeera that American-led forces bombed a clinic in Falluja.
"Insurgents have used allegations of civilian deaths as part of disinformation efforts in the past," Air Force 1st Lt. Marcella Hopp said in a written statement.
Newell said his troops continue to clear the city of suspected weapons caches and insurgents, and that they have found several booby-trapped areas.
In one area, the Army uncovered a weapons cache with two rocket-propelled grenades and 100 pounds of TNT explosive. In other places, soldiers found mortar systems, ammunition rounds and a bullet-proof vest.
In southern Falluja, soldiers found a notebook with photos believed to be of foreign fighters.
The assault on Falluja has not received unanimous support from Iraqis.
In a key political development, the Iraqi Islamic Party withdrew from the 100-person interim National Council in protest of the offensive.
"Military action against any city is the wrong answer and will not solve anything," said Mohsen Abdul Hamid, head of the group.
But interim Prime Minister Ayad Allawi, said Tuesday, "It is clear that, with the exception of a few extremists, the Iraqi people are fully behind the government's efforts to restore law and order, and to build the necessary security to hold elections in Iraq."
A city surrounded
By Monday, U.S. and Iraqi troops had surrounded Falluja as they awaited the order for a full attack in the latest attempt to subdue the city this year. (Gallery: Scenes from the field)
The aim of the Falluja assault is to root out insurgents ahead of scheduled January elections for a transitional national assembly.
The assault involves about 10,000 U.S. forces and more than 2,000 Iraqi troops, Pentagon officials said.
The Iraqi forces have "already acquitted themselves well," Metz said. They have been tasked with searching some of the city's 77 mosques, he said, where they have found "lots of munitions and weapons."
In April, Marines attacked Falluja after four U.S. private security contractors were killed and mutilated. The ensuing battles led to many deaths.
The U.S.-led forces pulled back and established an indigenous Falluja brigade to restore peace to the city, but in the summer, the brigade fell apart and insurgents solidified control there.
Falluja's population was estimated to be 250,000 to 300,000 before warfare escalated in the city this year. Now, it is thought that 50,000 civilians remain.
Other developmentsCharles Duelfer, the CIA's point man on weapons of mass destruction in Iraq, told CNN Tuesday he narrowly escaped death Monday when his convoy was attacked by insurgents on the road from Baghdad to the city's main airport. Two security guards were killed when two of the cars were fired on after insurgents blocked the road with a burning vehicle. "Where do all these kids who want to blow themselves up come from?" he asked. (Report: No WMD stockpiles in Iraq)Insurgents attacked two police stations Tuesday near Baquba, about 30 miles (50 kilometers) north of Baghdad, killing four people, while 15 people have died in separate incidents in the capital within 24 hours. (Full story)In Baghdad, Allawi imposed a citywide curfew that will run from 10:30 p.m. until 4 a.m. (2:30 p.m. to 8 p.m. ET). The curfew is the first in the capital since October 2003, and it was imposed indefinitely. In northern Iraq, at least three people died and several others were wounded in a suicide car bomb attack targeting an Iraqi national guard base north of Kirkuk, police said.
CNN's Jane Arraf, Arwa Damon, Kevin Flower, Jamie McIntyre, Bessem Muhy, Karl Penhaul, Cal Perry, Barbara Starr and Mohammed Tawfeeq contributed to this report.