The president was joined by his war cabinet and military commanders at an unprecedented meeting in Iraq over eight hours at this dusty military base in the heart of Anbar province, 120 miles west of Baghdad.
Mr. Bush did not say how large a troop withdrawal might be possible or whether it might occur before next spring when the first of the additional 30,000 troops he ordered to Iraq this year are to start coming home anyway. He emphasized that any cut would depend upon progress.
After talks with Gen. David Petraeus, the U.S. commandeer in Iraq, and Ambassador Ryan Crocker, Mr. Bush said they "tell me if the kind of success we are now seeing continues, it will be possible to maintain the same level of security with fewer American forces."
"If we're able to redeploy at some point in time - I would hope so," Mr. Bush told CBS Evening News anchor Katie Couric in Iraq. "Because the stakes are very high. Failure in Iraq could be a disaster for the United States."
Couric traveled with Petraeus this week to Fallujah in Anbar province, once a stronghold of the insurgency, and reports the troop surge appears to have helped quell much of the violence there.
Mr. Bush's trip was a dramatic move to steal the thunder from the Democratic Congress as it returns to Washington with fresh hopes of ending the unpopular war, now in its fifth year. Petraeus and Crocker will testify before lawmakers next week, and then Mr. Bush will announce how he intends to proceed in Iraq.
"The president was laying down his marker today," says CBS News chief Washington correspondent Bob Schieffer. "Congress comes back to Washington tomorrow demanding that he start withdrawing our troops from a very unpopular war."
The president thanked the 10,000 servicemen and -women, mostly Marines, stationed here in the sweltering 115-degree heat, reports Couric.
"What you're doing here is making this country safer and I thank you for your hard work," Mr. Bush said.
On Air Force One after leaving Iraq, Mr. Bush acknowledged that his comment about troop reductions had piqued interest. "Maybe I was intending to do that," the president said, sitting around a table with reporters in his plane's conference room as he flew to Australia to meet with Asia-Pacific leaders.
"If you look at my comments over the past eight months, it's gone from a security situation in the sense that we're either going to get out and there will be chaos, or more troops," the president said. "Now the situation has changed where I'm able to speculate on the hypothetical."
Still, Mr. Bush struck a defiant note about demands for bringing troops home.
Standing before troops cheering "hooah," Mr. Bush said decisions on force levels "will be based on a calm assessment by our military commanders on the conditions on the ground - not a nervous reaction by Washington politicians to poll results in the media.
"In other words," Mr. Bush said, "when we begin to draw down troops from Iraq, it will be from a position of strength and success, not from a position of fear and failure."