Over the weekend, Mr Howard met with the vice-president, Dick Cheney, and the Defence Secretary, Donald Rumsfeld.
The Prime Minister will spend the next three days in the United States meeting key officials.
Mr Howard says both he and Mr Cheney welcomed recent developments in Iraq including the selection of a new prime minister Nouri Al-Maliki.
"We all agree that the formation of a new government of national unity in that country would be very important and very positive."
He says; "And we're both of us of the view that the new nominee for the prime ministership of the country is a very positive thing. He's a person of great strength and experience."
Mr Bush and Mr Howard have shoveled dirt and planted a tree together at the Australian embassy in Washington as a symbol of the close Iraq war allies' friendship.
Mr Bush gave two White House trees -- an American elm and a southern magnolia -- to the Australian ambassador's residence in Washington.
"I think it is interesting that we're planting two trees, and this is a symbol of our enduring friendship," Mr Bush said after taking a shovel from a gardner and tossing soil at the base of the American elm.
"I can't thank you enough, John, for your strong support of the liberty agenda, deep desire for the world to be a peaceful place," he said. "I really enjoy working with you for the common good."
Mr Howard recalled that he had expressed support for the United States during a press conference at Australian ambassador's residence here on September 12, 2001, one day after the terror attacks that killed nearly 3,000 people in New York and Washington.
"I indicated to the president a moment ago that it was here on this lawn that I addressed a news conference on the 12th of September, 2001, when I said that Australia would stand side-by-side with the United States in responding to the new threat of terrorism," he said.
"And that resolve is as strong now as it was on the 12th of September, 2001," said Mr Howard, a staunch backer of the US-led war in Iraq.