By Matt Spetalnick

ABOARD AIR FORCE ONE, Sept 3 (Reuters) - After months of stubbornly refusing even to consider cutting U.S. troop levels in Iraq, U.S. President George W. Bush has suddenly decided the idea is no longer taboo.

He raised the possibility during a surprise visit to a desert air base in Iraq's Anbar province on Monday, saying there were signs of improved security and that some U.S. troops could be withdrawn from the country if the trend continued.

Even though he couched his words carefully and made no promises, it was the kind of concession rarely heard from Bush, who has made single-mindedness a defining trait of his presidency and of his conduct of the unpopular war in Iraq.

Bush may be trying to deflect some of the growing pressure he faces as he heads for a showdown with the Democratic-led Congress over his Iraq strategy.

Sitting down with reporters aboard Air Force One after seven hours of talks with U.S. and Iraqi officials on the ground, Bush held out the prospect that consultations on troop reductions could begin in weeks, if not days.

"The first moment that there will be any discussions about troop levels will be after General (David) Petraeus and Ambassador (Ryan) Crocker come back to Washington," Bush said, referring to their much-anticipated testimony before Congress next Tuesday to give their assessment of the situation in Iraq.

"Any announcement one way or another will be after these folks come back to report," he added as he flew to Sydney for an Asia-Pacific summit

Bush would not say how many troops could be withdrawn or how soon, and he insisted, as he has repeatedly, that any decisions would be based on the judgments of military commanders, not on political considerations in Washington.

But he made clear he saw a changing situation on the ground in Anbar and other parts of Iraq that had encouraged him to "speculate on the hypothetical" prospects for troop reductions.

SHOWCASING ANBAR

Bush spoke after hearing from Petraeus, the top U.S. commander in Iraq, and Crocker, the U.S. ambassador to Baghdad, who will testify about a troop buildup the president ordered earlier this year. There are now 160,000 U.S. troops in Iraq, including about 30,000 deployed since February.

Bush hailed what he saw as significant progress in quelling violence in Anbar, a former hotbed of the Iraq insurgency where Sunni tribal chiefs have joined with U.S. forces against al Qaeda militants.

Some Democrats say the president is trying to showcase a single area of achievement while ignoring broader failures by Prime Minister Nuri al-Maliki's Shi'ite-dominated government to promote national reconciliation needed to curb sectarian bloodshed.

The Bush administration has signaled it wants to maintain the higher force levels in Iraq well into 2008, but the president's latest comments indicate he may be open to some adjustments.

Bush acknowledged at the in-flight briefing that his current view marked a softening from months past, when he insisted any U.S. pullback would bring chaos in Iraq.

He may now be facing political reality at home. Democrats in control of Congress are ready to step up pressure for a withdrawal timetable, and even some of Bush's fellow Republicans are breaking ranks with him.

The latest was Republican Sen. John Warner of Virginia who recently called for some U.S. troops to be sent home by Christmas.

Bush's willingness to consider even modest troop reductions could prevent further Republican defections as the presidential campaign revs up and candidates worry about negative spillover from anti-war sentiment..

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