An influential Republican senator has called for the withdrawal of some 5,000 US troops from Iraq by the year's end.
There are more than 160,000 US troops in Iraq
Senator John Warner, former chairman of the Senate Armed Services Committee, said the US needed to show that its commitment to Iraq was not open-ended.
US troops, he said, had enhanced security in Iraq but had been let down by the Iraqi government.
He spoke after the release of a US intelligence report which said Iraqi leaders could not govern effectively.
The National Intelligence Estimate (NIE) acknowledged some military successes since January, following the "surge" in US troop numbers.
But it also said Iraqi security forces were still not capable of operating without support from American forces, and divisions between Sunnis and Shias continued to drive political instability.
It predicted that the situation would only get more precarious over the next six to 12 months.
The BBC's James Coomarasamy in Washington says that with political and public support for the war finely balanced in America, the words of a senior senator from President George W Bush's own party could have an important effect.
Senator Warner said initiating the first step in a withdrawal of US forces would send a clear message that Iraq's leaders should not take the presence of American troops for granted.
"We simply cannot, as a nation, stand and put our troops at continuous risk of loss of life and limb without beginning to take some decisive action which will get everybody's attention."
However the senator said that the president should establish a timetable for withdrawal, not the Congress.
The senator went on: "I say to the president, respectfully, pick whatever number you wish.
"You do not want to lose the momentum, but certainly in 160,000-plus, say, 5,000 could begin to redeploy and be home to their families and loved ones no later than Christmas of this year."
The NIE report represents the judgements of all 16 American intelligence agencies.
It was released a day after President Bush offered Iraqi Prime Minister Nouri al-Maliki his support, describing him as "a good guy doing a difficult job".
It also comes amid growing calls by senior US Democrats for Mr Maliki to step down because of his failure to bridge sectarian divides.
The report expresses grave doubts that Mr Maliki will be able to overcome sectarian divisions in Iraq and meet political benchmarks on unity.
"Levels of insurgent and sectarian violence will remain high and the Iraqi government will continue to struggle to achieve national-level political reconciliation and improved governance," it says.
Unless there is "a fundamental shift in factors driving Iraqi political and security developments," the political compromises needed for "sustained security, long-term political progress, and economic development are unlikely to emerge", it continues.
The report does say that "Sunni resistance to al-Qaeda has expanded in the last six to nine months, but has not yet translated into broad Sunni Arab support for the Iraq government, or widespread willingness to work with the Shia".
On Thursday, police reported that a Sunni religious leader in the province of Diyala who had encouraged his community to confront al-Qaeda had been killed in an attack by the militant group.
Mr Bush defended his Iraq policy on Wednesday, comparing current calls for withdrawal from Iraq with what happened at the end of the Vietnam War in 1975.
And following the release of the NIE report, White House spokesman Gordon Johndroe said: "Today's key judgements clearly show that the military's counter-insurgency strategy, fully operational since mid-summer, has begun to slow the rapidly increasing violence and patterns of the violence we have been seeing in Iraq.
"I don't think the president feels any differently about setting a specific timetable for withdrawal. I just think it's important that we wait right now to hear from our commanders on the ground about the way ahead."
A progress report is due in mid-September from General David Petraeus, the top US commander in Iraq, on the effectiveness of the recent surge in US troop numbers in tackling the violence there.