Even so, he declined to declare victory in the war in Iraq.
"I want to hear our commanders say we have achieved the clear objectives that we have set out. That's when we will say this is over," Mr. Bush told reporters Friday after visiting wounded servicemen and women in two military hospitals.
"We've had a historic week," he said. "I don't think I'll ever forget, and I'm sure a lot of other people will never forget, the statue of Saddam Hussein falling in Baghdad."
Mr. Bush said he prays that the Americans who had been held prisoner by Iraq are still alive. He said if they are, the U.S. military will find them.
The president's comments came as residents of Baghdad blockaded streets and beat up looters as disorder spread. The U.S. military instituted a curfew in areas under its control.
The northern Iraqi city of Mosul fell into U.S. and Kurdish hands Friday after an Iraqi army corps disappeared. Mosul, the largest city in northern Iraq, descended into anarchy, with looting, arson and shootings. U.S. Special Forces were sent in to restore order.
Saddam's hometown of Tikrit was the last major holdout of Saddam loyalists, but no major Iraqi troop units remained in the country, U.S. defense officials said at the Pentagon in Washington.
In other developments:
In Baghdad, the Ministries of Education and Industry were looted and set on fire, sending dark smoke over the city. The Foreign and Information Ministries and the Baath Party headquarters were sacked along with the city's engineering and nursing colleges. The Trade and Planning Ministries also were smoldering, along with one of the main markets in the city center.
Amid what it dubbed "anarchy and general chaos," the International Committee of the Red Cross said it "fears that the hospitals in Baghdad are no longer functioning and have been largely deserted by staff and patients." The Al-Kindi hospital has reportedly been looted of beds and equipment.
"Tell the Americans to stop the killing and the looting," pleaded one Baghdad woman, Jabryah Aziz, 41. "We can't live like this much longer, with Muslims looting other Muslims."
U.N. Secretary-General Kofi Annan said the Geneva Conventions stipulate that preventing looting is a responsibility for the occupying force, meaning the Americans and the British.
Central Command spokesman Brig. Gen. Vincent Brooks said U.S. forces were trying to get control without repressing recently liberated Iraqis. "We are not exercising the same kind of grip on the population that the regime did. That's by design," he said.
Officers with the 7th Marine Regiment said they received orders Thursday night to try to stop looting. The regiment planned to enforce a dusk-to-dawn curfew Friday in the area it patrols in eastern Baghdad.
American troops still face enemy fighters in the capital. In the Al-Mansour district in western Baghdad, pro-Saddam bands of Arab volunteers manned sandbagged positions, armed with rocket-propelled grenades and Kalashnikov rifles. Residents said they were mostly Syrians.
On Friday, a car carrying an Iraqi family drove through a checkpoint in Baghdad without stopping, and Marines opened fire. Three adults were killed, and a 5-year-old girl was wounded.
On Thursday night, a vehicle containing explosives was driven to a checkpoint near the Saddam City section of Baghdad and detonated, Brooks said. Four Marines and one medical corpsman were wounded, he said, without providing details.
A short time later, soldiers killed a man who approached a checkpoint and did not heed orders to stop. He turned out to be unarmed.
In Washington, Defense Secretary Donald H. Rumsfeld characterized the widespread looting in Iraq as a period of "untidiness" and suggested it was only a transitional phase on the way to freedom from Saddam's rule.
"If you go from a repressive regime...in that transition period, there is untidiness," he told a Pentagon news conference.
Rumsfeld said coalition forces were providing security for Iraqi citizens and stopping looting when they see it.
He said he didn't know if Saddam was dead or alive. "If I had a conviction, I would say so and I don't. And I see a lot of information," he said.
Rumsfeld also said he wasn't surprised that biological or chemical weapons have not yet been uncovered, suggesting they are deeply hidden somewhere.
"It's a big country," he said. "We're going to find the people" who can help lead allied forces to them, he added.