But he refused on Thursday to set a timetable for withdrawing American troops.
"I believe we're making really good progress in Iraq," Bush said. "They saw a government form today. The Iraqi military is being trained by our military, and they're performing much better than the past."
Iraq on Thursday formed its first democratically elected government in more than 50 years, ending three months of political stalemate that has hampered efforts to tackle violence.
Bush said he spoke to Prime Minister Ibrahim al-Jafari earlier on Thursday and invited him to the US.
"I told him I was proud of the fact that he's willing to stand up and lead. I told him I appreciate his courage and the courage of those who are willing to serve the Iraqi people in government," he said at an evening news conference.
The US has reduced the number of troops in Iraq to 139,000 from 160,000, and the deployments have not stretched the armed forces too thin to operate elsewhere if needed, Bush said.
"I know there's a temptation to try to get me to lay out a timetable [for withdrawal]," Bush said. "I don't think it's wise for me to set out a timetable. All that will do is cause an enemy to adjust."
The anti-US uprising remains as
potent as it was a year ago
US troops would be pulled out of Iraq "as soon as possible", he said. "And as soon as possible depends upon the Iraqis being able to fight and do the job," he added.
US forces invaded Iraq in March 2003 and toppled Saddam Hussein, but a violent anti-US campaign has taken hold that has killed American troops and Iraqi civilians.
General Richard Myers, chairman of the Joint Chiefs of Staff, earlier this week said Iraq's uprising remained undiminished in its capabilities in the past year despite US-led efforts to crush it.
Bush said: "There are still some in Iraq who aren't happy with democracy. They want to go back to the old days of tyranny and darkness and torture chambers and mass graves."
But he said he told al-Jafari that the US had made a commitment to Iraq and would stand by it.
US officials point to the democratic moves in Iraq as a sign that democracy can spread more broadly in the Middle East.
"A free Iraq in the midst of the Middle East is an important part of spreading peace," Bush said. "It's a region of the world where a lot of folks in the past never thought democracy could take hold," he said.
"And in order to defeat the terrorists, in order to defeat their ideology of hate, in the long run we must spread freedom and hope," Bush said.