"If I didn't think we could succeed, I wouldn't have our troops there," he said.
Bush said it was important "that we hang in there with the Iraqis and help them."
Australia participated in the US-led invasion of Iraq in 2003 and still has about 1,600 troops in and around the country, 550 of them in combat roles. Yet the war remains unpopular here, and Howard faces an aggressive challenge in elections expected to be called within three months.
Polls show Howard, in office for 11 years, trailing opposition leader Kevin Rudd, who has promised to pull combat troops out of Iraq if he wins. Howard has refused to set a deadline.
Bush, who meets with Rudd tomorrow, has urged coalition partners to make decisions based on conditions on the ground rather than on internal politics. He has voiced strong support for Howard, calling him "a man of steel." Howard has been equally effusive about Bush.
Howard is the last leader among the major original "coalition of the willing" partners still serving. Among those who paid a political price for standing with Bush on the war are former prime ministers Tony Blair of Britain, Silvio Berlusconi of Italy, and Jose Maria Aznar of Spain.
En route to Australia, Bush made an unannounced stop in Iraq, meeting Monday with Iraqi government and Sunni tribal leaders, US troops and their commanders at a military base in the heart of Anbar Province, 120 miles west of Baghdad and once rife with Sunni insurgents. He was joined by his war cabinet.
Bush emphasized his belief that his current strategy which increased US troop levels this year by about 30,000 to a total of 160,000 was working and he raised the possibility of US troop cuts if violence continues to ease. He reiterated his belief that troop-level decisions must be based on conditions on the ground and recommendations from military commanders.
Bush's visit to Iraq was an attempt to get out in front of an expected confrontation with Congress, and a progress report due next week from General David Petraeus, the US commander in Iraq and US ambassador to Iraq Ryan Crocker.
