The US troops cheered loudly and raised cameras high as Bush visited them.

"Thought I'd stop by to say hello," Bush said, to laughter. "I bring greetings from a grateful nation. And I thank you for your sacrifice."

Bush's visit came as his administration attempted to regain the initiative after months of increasingly deadly violence in Iraq and flagging support for the war among Americans.

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 US 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."

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

But underscoring the dangers that remain, a series of explosions struck the northern city of Kirkuk on Tuesday, killing at least 16 people. And the new leader of al-Qaida in Iraq pledged to avenge predecessor al-Zarqawi's death with horrific attacks, according to a statement posted on the Web.

Al-Maliki has won US admiration by promising to crack down on militias and sectarian violence, promote national reconciliation, accelerate reconstruction efforts and restore essential services such as electricity.