President Bush says Saddam Hussein's regime is "passing into history," though coalition forces may still face fierce combat.

"The conflict continues in Iraq, and our military may still face hard fighting. Yet the statues of the dictator and all the works of his terror regime are falling away," the president said Saturday in his weekly radio address.

The remarks capped a week in which U.S. troops seized Saddam's capital, raided his palaces and -- providing an image that symbolized the collapse of his regime -- helped jubilant Iraqis rip a statue of their toppled leader from its pedestal.

"Over the last several days, the world has watched as the regime of Saddam Hussein began passing into history," Bush said. "We will always remember the first images of a nation released from decades of tyranny and fear."

Bush taped the address Friday before visiting wounded U.S. troops and later flying to the Camp David presidential retreat for the weekend.

On a tearful tour of the two Washington-area military hospitals, Bush met with 75 injured troops, handed out 10 Purple Hearts and watched two servicemen -- one from Mexico, the other from the Philippines -- be sworn in as U.S. citizens.

Citizenship for one of them, Lance Cpl. O.J. Santa Maria, was expedited as a result of an executive order Bush signed last year that allowed faster naturalization for anyone involved in military hostilities.

Suffering visibly from a shoulder wound received in Nasariyah and hooked up to a blood transfusion, Santa Maria managed to stand -- over protests -- for the ceremony. Halfway through, he broke down sobbing from the pain and the occasion.

"We're proud to have you as an American," Bush told him, according to press secretary Ari Fleischer. "I'll never forget this moment."

One soldier, badly injured by a rocket-propelled grenade, thanked Bush for "allowing us to do our jobs."

"Were you ready?" Bush asked.

"Hell, yes," the soldier replied. "I'll do it again when I'm ready."

The White House did not provide the soldier's name.

Speaking to reporters afterward, Bush said he is not ready to declare victory in Iraq nor end the fighting even with Saddam "no longer in power."

"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," Bush said.

White House officials said there is no guarantee that Bush will ever formally declare the war over, and he certainly won't do so any time soon, in part because a premature declaration would open him to criticism if more casualties follow.

Instead, aides said Bush could bask in a series of victories -- the first meeting of potential leaders of a new Iraq, expected to be held in the next 10 days; free flow of humanitarian goods; the formation of an interim authority to govern Iraq; and the election of a new government.

Bush used his radio address to pledge anew that coalition forces will help Iraq recover from war and create a democratic government -- then leave.

"Soon, the good and gifted people of Iraq will be free to choose their leaders who respect their rights and reflect their character," the president said.

"As people throughout Iraq celebrate the arrival of freedom, America celebrates with them," he said.