"It's going to take awhile, but it's a necessary part of the development of a free society," Mr. Bush said at a White House news conference with visiting Australian Prime Minister Kevin Rudd. At the same time, the president said the situation in Iraq remains "dangerous and fragile."
His comments followedin both the southern city of Basra and in a Shiite militia stronghold in Baghdad. The renewed violence came as tensions rose among followers of radical Shiite cleric Muqtada al-Sadr angry over a crackdown that has threatened to unravel a militia cease-fire.
"Basra has been a place where criminality has thrived," Mr. Bush said. "They are fighting some pretty tough characters... and yes, there's going to be violence, and that's sad."
He said the resurgent violence would not alter his determination to continue his administration's mission there.
"Any government that presumes to represent the majority of people must confront criminal elements or people who think they can live outside the law. That's what's taking place in Basra and other parts of Iraq," Mr. Bush said. "I would say this is a defining moment in the history of Iraq."
"There have been other defining moments up to now, but this is a defining moment, as well," Mr. Bush said. He said the decision to move troops into Basra was testimony to Prime Minister Nouri al-Maliki's leadership capabilities.
"This is a good test for them," the president said.
"I'm confident we can succeed unless we lose our nerve," he added. "It's going to take a while for them to deal with these elements."
Mr. Bush also suggested that his Iraq policy was working because "troops are coming out."
The new Australian prime minister campaigned on a theme of withdrawing Australian troops from Iraq. Mr. Bush brought up Rudd's Iraq stance himself in his opening remarks.
Asking and answering his own question, Mr. Bush said he expected a journalist to ask him, "Aren't you mad at the prime minister for fulfilling his campaign pledge? The answer is no."
"I always like to be in the presence of somebody who does what he says he's going to do ... Here's a guy who meant it ... He consulted closely with his friends. His military commanders consulted closely with our military commanders," Mr. Bush said.
The president noted, however, that Australia continues to have troops in Afghanistan and is helping to train Iraqi farmers in dry-land farming.
For his part, Rudd said, "We're in Afghanistan for the long haul."
The two leaders were asked about civil unrest in Tibet and China's crackdown there and both urged China's leaders to meet with representatives of the Dali Lama to discuss the violence.
"It is absolutely clear that there are human rights abuses in Tibet," Rudd said. "It's clear-cut; we need to be upfront and absolutely straight about what's going on."
Mr. Bush said he told Chinese President Hu Jintao this week that "it's in his country's interest" that top Chinese leaders meet with representatives of the Dalai Lama, Tibet's exiled spiritual leader.
"We urge restraint," Mr. Bush said.
On relations with Australia, said he expects them to "strengthen and endure" under Rudd.
"I don't see differences when it comes to foreign policy," Mr. Bush said. Even so, both worked to smooth over Australia's decision on Iraq.
Mr. Bush called Rudd a "straightforward fellow" and Rudd called the president "George" and joked with Mr. Bush about being from Queensland in northeast Australia, which has similar terrain as Texas.
Rudd said that after he asked Iraqi Prime Minister Nouri al-Maliki how Australia could help in nonmilitary ways, his country decided to send $165 million to Iraq, the bulk of which will go to help train Iraqis on dry-land farming.