Pentagon officials say American forces will focus their attacks on the northern regions in the days ahead, including Saddam Hussein's hometown of Tikrit, about 100 miles north of the capital.
On Thursday, America's Kurdish allies entered the northern city of Kirkuk. The extent of pro-Saddam resistace was unclear in the city, which is near some of the country's most productive oil fields.
The United States is worried that Iraqis have wired explosives to wells and other facilities in oilfields in northern Iraq, ready to cause an environmental disaster.
Ten or more Iraqi army divisions — as many as 80,000 troops — were in the area between the capital and the Kurdish-controlled areas of far northern Iraq, Joint Chiefs of Staff Chairman Gen. Richard Myers said Wednesday. Other military officials said some surviving Iraqi units had converged on Tikrit, home to Saddam's relatives and presumably his most die-hard supporters.
Whether those Iraqis were willing or able to put up much of a fight was unclear, however. Pentagon officials say Iraqi military lines of communication were severed and they saw no evidence Iraqi forces were getting any direction from above or working in any coordinated manner. Earlier this week, Myers said all but a few dozen Iraqi Republican Guard tanks had been abandoned or destroyed.
Despite the heavy U.S. military presence in Baghdad, pockets of the capital remain outside coalition forces' control.
"Baghdad's still an ugly place," said Maj. Gen. Gene Renuart, director of operations at the U.S. Central Command.
"That's really the objective of our operations in Baghdad right now — is to go to those locations and return some stability," Renuart said.
"We are succeeding each day to secure more and more of the city," he added.
U.S. forces fought at least two fierce battles in Baghdad on Wednesday and Thursday, including one on the campus of the University of Baghdad and a three-hour firefight at one of Saddam's palaces.
And in northern Baghdad's Imam Mosque, Iraqi fighters opened fire Thursday on U.S. Marines who were hunting for regime leaders, triggering a fierce battle.
Marines from the 1st Marine Expeditionary Force had been scouring the area after U.S. officers received a tip that regime leaders were trying to organize a meeting there, at the house of a senior Baath Party official.
The "intense fighting" took place near the Az Amihyah Palace and party official's house, Central Command spokesman Frank Thorp said. He did not have information on casualties, although officers in the area reported one Marine killed and up to 20 others wounded in fighting at the palace.
Still, defense officials warned that the war was not over.
"There's a lot more fighting that's going to be done," Defense Secretary Donald H. Rumsfeld told reporters at the Pentagon. "There are more people that are going to be killed, let there be no doubt. This is not over, despite all the celebrations on the street."
Coalition forces also must capture "or otherwise deal with" Saddam and his sons Qsay and Odai, Rumsfeld said.
American special operations forces on Wednesday scoured the site in a Baghdad neighborhood where four tons of U.S. bombs obliterated a building where Saddam was believed to be staying.
The team was looking for remains and other evidence, such as Saddam's personal effects, that would indicate the Iraqi president was inside the building when the bombs hit on Monday.
Rumsfeld said he didn't know whether Saddam and his sons escaped the bombing, and he made no promises about finding the Iraqi leader.
Rumsfeld and Myers attempted to strike a balance between celebration and caution, declaring the Iraqi president's rule all but dead but also emphasizing that much remained to be done before U.S. troops could go home.
Rumsfeld listed eight missions in Iraq that must be completed "before victory can be declared."
Senior White House officials, speaking on condition of anonymity, said there was no checklist that must be completed before Mr. Bush declared victory. The end could come before some of Rumsfeld's stated missions were achieved, possibly including the confirmation of Saddam's fate, they said.
Rumsfeld listed these other remaining U.S. tasks besides dealing with Saddam:
Discovering more about how Saddam built his weapons programs and locate Iraqi scientists with knowledge of them. He said U.S. government rewards were being offered to further those goals: capturing or killing terrorists still operating in Iraq; finding members of Saddam's Baath Party and their records and weapons caches; and locating records of the Iraqi intelligence service and other security organizations and paramilitaries.
Working with Iraqis, including those returning from exile, to establish an interim government authority.
The air campaign in Iraq was slowing somewhat, now that Baghdad's resistance has been broken. And the 4th Infantry was still assembling in Kuwait and preparing to join the fight in central or northern Iraq, a senior defense official said Wednesday.