President Bush met with Iraqi exiles Friday in an attempt to illuminate the horror of life under Saddam Hussein's regime, not focus on a plan for governing of Iraq after he is deposed.

"The meeting with the free Iraqis and the Iraqi-Americans today is a reminder to people about how much people care about freedom and liberty and how the voices of those who are fortunate enough to have left Iraq and who can speak freely, without being tortured or killed, that these voices here in America represent the voices of the people living inside Iraq today," White House spokesman Ari Fleischer said before the meeting.

Meeting privately with a dozen Iraqis and Iraqi-Americans, the president heard stories about jailings, beatings, torture and execution. One visitor to the White House said they offer only a glimpse of the suffering by Iraq's citizens.

Maha Hussain, who fled Iraq in the 1980s after two cousins were executed by the regime, added that she is not surprised that Saddam's regime had shot people who surrendered to U.S.-led troops or that Iraqis were forced to be human shields.

It's merely a continuation of the atrocities Saddam has been perpetrating for 34 years, Hussain said.

But as the exiles recounted the tragedies, Fleischer said the president is not ready to name who will be running the country after the conflict — particularly because the conflict isn't over. He said the decision will be made by Iraqis.

"The president has said that it should be a matter for Iraqis from both inside and outside Iraq to govern their country, and the territorial integrity of Iraq must be maintained. That's our approach," Fleischer said, adding that the United States will be there to help the nation get back on its feet.

Defense Secretary Donald H. Rumsfeld is said to be leaning toward an interim Iraqi government led by exiles. In a memo prepared for the White House this week, Rumsfeld called for quick action and said those who have been living outside the torment of Saddam are probably better prepared to take up the reins of democracy.

But the White House has apparently rejected that idea. National Security Adviser Condoleezza Rice told reporters Friday that residents from within the country must be included in an interim — or transitional — governing authority.

"The interim authority will be a transitional authority run by Iraqis until a legitimate permanent government in Iraq is established by the Iraqi people. It will be broad-based, drawing from all of Iraq's religious and ethnic groups, including Iraqis currently inside and outside of Iraq. It will be a means for Iraqis to participate immediately in the economic and political reconstruction of their country," she said.

Rice, however, did cede to Pentagon suggestions that an interim government be established in some parts of the country even before Baghdad falls. And she said that the United Nations will play an undetermined role in the interim authority. But she said countries that fought the war will dominate the postwar process.

"Having given life and blood to liberate Iraq ... the coalition intends to have a leading role," she said.

According to the Pentagon, the Iraqi people are less afraid of Saddam now that the coalition has had such dramatic successes. More Iraqis are said to be asking troops to stay and to tell them "what time Saddam is finished."

Iraqi officials maintain that Saddam is still in control, playing video on Iraqi television Friday that shows Saddam walking through the streets of Baghdad among throngs of cheering people.

The scene, near a memorial site that honors the unity of Palestinian and Iraqi people, shows him moving around easily. Officials said the fact that there is smoke in the background leaves a high probability that it is a relatively recent tape.

Officials said the thinking is that the person walking around is probably not a body double. The Pentagon targeted Saddam on the first night of the bombing campaign, and has not been able to say since whether he is dead or alive.

Fleischer said that the United States would consider military action in Iraq to be a success even if Saddam is never found. He said what's important is that the regime be disarmed and changed so the Iraqi people can be liberated.

"I can also tell you in the bigger scheme of things it really doesn't matter, because whether it is him or whether it isn't him, the regime's days are numbered and are coming to an end," he said.

As the push to Baghdad continues and Iraqi independence draws nearer, the president is preparing to meet with British Prime Minister Tony Blair next week to discuss humanitarian aid for the Iraqi people and rebuilding Iraq. The two will also discuss the Middle East peace process, which Blair says is essential to move forward and winning support for the Iraq mission.

Fox News' Wendell Goler and Kelly Wright contributed to this report.