"We simply cannot as a nation stand and continue to put our troops at continuous risk of loss of life and limb without beginning to take some decisive action," Warner told reporters after a White House meeting with Bush's senior aides.
"Had the US foreign policy makers read history, they would not get involved in any war after Vietnam"
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Warner, who visited Iraq this month with Carl Levin, the Democratic senator who chairs the senate Armed Services Committee, was clearly not pleased with al-Maliki's failure to unite his government during the recent US "surge" to control sectarian violence.
"I really believe Prime Minister Maliki let our troops down and the NIE confirms that," he said, referring to the National Intelligence Estimate, the collaborative judgment of 16 US intelligence agencies, including the CIA.
The former navy secretary and second-ranking Republican in the senate Armed Services Committee, is against Democratic demands for a full withdrawal timetable.
"I don't for a minute advocate any type of rapid pullout," he said, adding that he was "not in any way trying to pull the rug out from under the troops".
But "say 5,000 could begin to redeploy and be home not later than Christmas of this year" to let Baghdad know that the US is not pleased with the lack of political progress.
White House response
A White House spokesman, Gordon Johndroe, declined to say whether Bush might consider Warner's suggestion.
"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," he said.
The top US commander in Iraq, General David Petraeus, is set to deliver his assessment of the war in September.
Warner's statement came just 24 hours after the president made his case for staying the course in Iraq and reaffirmed support for the Iraqi prime minister.
On Wednesday Bush had warned again that leaving Iraq could lead to a parallel with Vietnam where he said the legacy of America's withdrawal was a heavy price paid by millions of Vietnamese citizens.
The Vietnam analogy was also used by US intelligence analysts on Thursday: warning that fighters in Iraq may be planning a massive Tet offensive-style attack against US troops – a reference to the disastrous attack against US forces by the Viet Cong that signalled the beginning of the end of US involvement in the Vietnam war.
The NIE said in a report released on Thursday that the Iraqi government was failing to deliver political solutions needed to begin solving the country's problems, including the incessant violence.
The report concluded that Iraq's political leaders remain unable to govern effectively and that the country's sectarian groups have still not reconciled.
It also said that Nuri al-Maliki's government would become more vulnerable in the coming months.
It pointed to a series of "uneven improvements" in Iraq - progress in financial and economic matters but still a high number of attacks on civilians and clashes between sectarian groups.
And Iraqi security forces had not shown they could operate independently from US-led forces on a regular basis and that a change in their joint mission or taking US troops out of Iraq would increase the violence, it said.