Bush's visit came six days after a U.S. air strike killed al-Qaida terror chief Abu Musab al-Zarqawi and five days after Iraqi Prime Minister Nouri al-Maliki completed his cabinet by naming the ministers of Defense and Interior -- events the president's advisers hoped would lead to political progress.

Bush said he made the surprise trip to Baghdad to size up al-Maliki and members of his cabinet. The president came away with a good impression of al-Maliki and his team, which combines Sunni, Shiite and Kurd officials into a unity government.

"I wanted to hear him talk about his way forward in Iraq," Bush said. "I wanted to hear whether or not he was stuck in the past or willing to think about the future. I wanted to get a sense of his capacity to prioritize and rally people to achieve objectives. I came away with a very positive impression. He was a serious-minded fellow who recognized there had to be progress in order for the Iraqi people to believe the unity government could make a difference in their lives. He specifically talked about electricity in Baghdad and we talked about the security situation."

Bush listened to individual cabinet members describe the challenges they face. He referred to them by their jobs -- "oil guy," "reconciliation person," "defense minister," "the electricity man," a "lady member of the cabinet" who talked about human rights concerns about coalition forces.

"I came away with the feeling they're plenty capable people," the president said.

Bush didn't say whether he and the prime minister had discussed the timing or scope of a possible U.S. military withdrawal. Al-Maliki, speaking in Arabic, thanked Bush for U.S. protection, but expressed a general hope for the day when American troops would be gone.

"God willing, all of the suffering will be over, and all of the soldiers will be able to return to their countries with our gratitude for what they have offered," al-Maliki said.

Before leaving Baghdad, Bush addressed a group of about 300 cheering U.S. troops assigned in supporting roles to the U.S. Embassy. He thanked them for their work and said a top U.S. priority was now to support the new government.

"Our job is to help them succeed and we will," Bush said.

In Washington, Secretary of State Condoleezza Rice and Defense Secretary Donald H. Rumsfeld gave a classified briefing on Bush's trip to selected senators.

Sen. Carl Levin of Michigan, senior Democrat on the Armed Services Committee, told reporters afterward that Bush's trip "is likely to lead to phased redeployments this year and continuing in the next year."

Rumsfeld said that many U.S. troops have already been brought home. He said officials would meet with Iraqi leaders "in the weeks ahead discussing at what pace we're going to be able to draw down our forces and it will all be done in a very orderly way."