Bush arrived in Sydney late on Tuesday ahead of summit of the 21 nation Asia-Pacific Economic Co-operation (Apec) forum this week.
With Bush and the presidents of Russia, China and other regional leaders in attendance, Australia has deployed its largest ever security operation for the summit.
Some 5,000 police and special forces are being deployed in and around Sydney in anticipation of demonstrations from anti-war groups and other protesters.
Howard's comments came as the senior US military commander in Iraq hinted that he may recommend a reduction of US troops by March 2008.
|Bush's visit has drawn anti-war protests |
on to the streets of Sydney [EPA]
The comments from General David Petraeus echoed similar remarks made by Bush on Monday during a visit to Iraq on his way to Australia.
Speaking to reporters on Wednesday, Howard reaffirmed his close support for US policy.
"We believe that at a time like this, a close ally and friend such as Australia should be providing the maximum presence and indication of support to our very close ally and friend in the president of the United States," he said.
For his part, Bush said he saw security and political progress in Iraq and vowed to "hang in there" despite pressure to pull US forces out.
"If I didn't think we could succeed, I wouldn't have our troops there"
"If I didn't think we could succeed, I wouldn't have our troops there," he said. "There's more work to be done. But reconciliation is taking place."
Australia has about 1,500 troops on operations in support of the war, about 550 of whom are employed in combat roles.
But the Australian government's support for the war has hit Howard hard in opinion polls ahead of national elections due this year.
Latest polls show Kevin Rudd, Australia's opposition leader, ahead of Howard by as much as 18 points.
Bush is expected to hold separate talks with Rudd later in the week
As host of the annual Apec meeting, Howard has put a declaration on climate change high on the summit agenda.
|Plans to tackle climate change are high on |
the Apec summit agenda [GALLO/GETTY]
Bush, who has been criticised for his opposition to the Kyoto Protocol regulating greenhouse gas emissions, was expected to push for a new climate change deal more to his liking.
Speaking after his talks with Howard on Wednesday, he urged Apec nations to band together on the issue, saying that China and all other major polluters must be part of any effective solution.
"For there to be an effective climate change policy, China needs to be at the table," Bush said after Wednesday's talks with Howard.
"In order to get China to the table they have to be a part of defining the goals."