Bush spoke live to the nation, and to US soldiers in Baghdad Bush speech in full

Mr Bush said 5,700 personnel would be home by Christmas, and expected thousands more to return by July 2008.

He said he had accepted the advice of US commander in Iraq, Gen David Petraeus, who gave a progress report to Congress earlier this week.

The plan would take troop numbers back to their level before Mr Bush ordered a "surge" at the start of this year.

The Democrats had called for a change of course, accusing the president of giving no plan on how to end the war.

And, says the BBC's Justin Webb in Washington, they reacted to this speech with unusually strong condemnation. One presidential candidate, Joe Biden, called it shameful and bizarre.

Mr Bush's speech followed the news that a key Sunni ally of the US had been killed in Iraq.

'Never too late'

In his primetime televised address, President Bush announced plans to reduce US troops by roughly 30,000 by next summer, if certain conditions were met.

It is never too late to support our troops in a fight they can win President Bush Analysis: No change of course Bush speech: Full text In quotes: Political reaction

"The more successful we are, the more American troops can return home," he said.

He argued that the gradual pull-out plan bridges the gap between the people who want to bring troops home, and those who believe success in Iraq is essential to US security.

"[The strategy] makes it possible, for the first time in years, for people who have been on opposite sides of this difficult debate to come together."

Addressing the critics of the war, he said: "It is never too late to deal a blow to al-Qaeda. It is never too late to advance freedom. And it is never too late to support our troops in a fight they can win."

Among the key points of Mr Bush's speech were:

• Troop reductions to start this month with 5,700 fewer personnel in Iraq by Christmas, and the number of combat brigades to fall from 20 to 15 by July 2008
• The transition to next phase of Iraq strategy to begin in December, with US troops moving towards a support role for the Iraqi army
• A free Iraq would be an "anchor for stability" in the region, countering the "destructive ambitions" of Iran and denying al-Qaeda a safe haven
• Sunni Muslims battling the al-Qaeda insurgency can continue to rely on the support of the US

BBC diplomatic correspondent Jonathan Marcus says Mr Bush is trying to disarm domestic critics, especially those in his own Republican Party.

However, beneath the rhetoric, our correspondent says, Mr Bush clearly has no intention of changing course and the withdrawal from Iraq looks set to be the top item on the agenda for the next president in January 2009.

I think we've turned the corner in Iraq and are heading into a new place Mitch McConnell Senate Minority Leader US press analyses speech Send us your reaction

Democrats quickly rounded on the speech.

Senate Majority Leader Harry Reid said it was "just more of the same", House Speaker Nancy Pelosi that it meant a "10-year occupation of Iraq" and Sen Hillary Clinton that is was "simply too little too late".

Sen Jack Reed said: "Once again, the president failed to provide either a plan to successfully end the war or a convincing rationale to continue it."

But a number of Republicans praised Mr Bush for listening to the recommendations of Gen Petraeus.

Senate Minority Leader Mitch McConnell said: "I think we've turned the corner in Iraq and are heading into a new place."

Representative Jim Gerlach said: "It's time Speaker Pelosi and Senate Democrat leader Reid halt their daily, partisan attacks."

Tribes' resolve

President Bush's speech comes after the death of Abdul Sattar Abu Risha, who led what was known as the "Anbar Awakening", an alliance of Sunni Arab tribes that rose up against al-Qaeda in Iraq.

PETRAEUS - KEY POINTS Sectarian violence declined since surge started 30,000 US troops likely withdrawn by mid-2008 Decision on further troop cuts expected in March Situation in Iraq remains difficult Key quotes from hearing General Petraeus: Report to Congress [64 KB] General Petraeus: Report charts [1 MB] Ambassador Crocker: Report to Congress [50 KB] Most computers will open these documents automatically, but you may need Adobe Reader Download the reader here

He met and was endorsed by Mr Bush when the president visited US troops in Iraq last week. The White House has condemned his killing in a bomb attack.

Correspondents say his death may undermine US efforts against al-Qaeda in Anbar province, or strengthen the tribes' resolve to maintain an alliance with the US and Iraqi government.

The withdrawal plan would bring the number of US troops in Iraq down from a current high of more than 160,000, to "pre-surge" levels of about 130,000.

Observers point out that the surge would have had to come to an end next spring anyway, in order to avoid overstretching the military.

The Democrats have so far been unable to pass legislation to set a timetable for withdrawal from Iraq because their majority in Congress is too slim to overturn a presidential veto.