"My attitude is if he didn't want to continue the drawdown, that's fine with me," Bush said.
"The only thing I can tell you is we're on track for what we've said was going to happen," he said, referring to plans to withdraw some 30,000 troops from Iraq by July.
Bush is in Kuwait on the first leg of a visit to the Gulf. He will also be visiting Bahrain, the United Arab Emirates, Saudi Arabia and Egypt.
During the trip he hopes to persuade the Arab nations to assist with the Israel-Palestine peace process and help contain Iran.
General David Petraeus, the commander of US forces in Iraq, and Ryan Crocker, the US ambassador to Baghdad, met Bush on Saturday at Camp Arifjan.
About 9,000 US troops are based at Camp Arifjan, one of the largest US military bases in the region.
Bush defended his decision a year ago to order a buildup of troops to Iraq.
"The new way forward I announced a year ago changed our approach in fundamental ways," he said. "Iraq is now a different place from one year ago."
"Levels of violence are significantly reduced. Hope is returning to Baghdad," he said, adding that the al-Qaeda network in Iraq had been "dealt heavy blows".
He arrived in Kuwait on Friday and had dinner with, Sheikh Sabah al-Ahmad al-Sabah, Kuwait's ruler, who thanked Bush for his efforts in progressing key Middle East issues.
Media in Kuwait said officials would tell Bush of their concerns that a US strike on nearby Iran would destabilise the Gulf, which is crucial to world oil supplies.
Such as message is likely to be repeated to Bush by his other hosts on the Gulf state tour.
Kuwait has said it will not allow the US to use its territory for any strike against Iran.
Bush said that Iran posed "a threat to world peace" and should not be allowed to develop expertise to produce nuclear weapons, in Israel on Wednesday.
Iran has denied wanting to build nuclear weapons.
Some commentators have said that Washington could take military action against Iran to prevent progression with its nuclear programme.
Bush will fly to Bahrain later on Saturday.
A visit by Bush to Iraq during his current tour has not been ruled out.
Bush has been to Iraq three times since he ordered the invasion of the country in March 2003, most recently in September last year.