Mr Bush hinted at a possible reduction in the numbers of US armed forces personnel in the troubled country, during his trip to the al-Asad airbase in Anbar province.
VIDEO: Fleeting visit
But he insisted any alteration in the soldiers' presence would be based on the recommendations of his commanders in Iraq, rather than "nervous" politicians at home.
"Those decisions 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," the president said.
"In other words, when we begin to draw down troops from Iraq, it will be from a position of strength and success, not from the position of fear and failure."
His visit came as British troops pulled out of their base at Basra palace, handing over to Iraqi soldiers, and withdrawing to a new headquarters at the city's airport.
The President's Iraq strategy is under fire in the US too, with leading Democrat Hillary Clinton vowing to bring troops home if she captures the White House next year.
US commander General David Petraeus and US Ambassador Ryan Crocker are due to report to congress on the progress of the troop "surge" strategy next week.
"General Petraeus and Ambassador Crocker tell me if the kind of success we are now seeing continues, it is possible to maintain the same level of security with fewer American forces," Mr Bush said.
Mr Bush also met embattled Iraqi Prime Minister Nuri al-Maliki and other Iraqi leaders for a "war council" during his unexpected trip.