"More of Iraq's people are seeing the benefits a Democratic society can bring," Mr. Bush said.
But he conceded that stubborn security challenges remain.
"The terrorists and Saddamists have been able to slow progress but they haven't been able to stop it," the president said in a speech to the Council on Foreign Relations.
Mr. Bush's address was the second in a series of four to answer criticism and questions about the continuing U.S. presence in Iraq more two and a half years after the war started.
It was an attempt by Mr. Bush to rebuild trust on Iraq and acknowledge for the first time that mistakes have been made, and, more importantly CBS News chief White House correspondent John Roberts reports, point out he has learned from them.
In particular, Mr. Bush cited Najaf, 90 miles south of Baghdad, and Mosul in northern Iraq — once the sites of some of the bloodiest battles of the war — as two cities where headway is being made, giving Iraqis more of a stake in their country's future.
"In places like Mosul and Najaf, residents are seeing tangible progress in their lives," Mr. Bush said. "They're gaining a personal stake in a peaceful future and their confidence in Iraq's democracy is growing. The progress in these cities is being replicated across much of Iraq."
But even the more sober assessments don't tell the whole story in Iraq. Electricity is still below pre-war levels, Roberts reports. Clean water and sewage remain a problem in much of the country and more than half of Iraqis are still unemployed or underemployed.
In a recent CBS News/New York Times Poll, President Bush's approval ratingsto 40 percent, but he is still in the midst of his lowest job approval rating of his presidency.
The latest series of speeches amount to a public relations campaign to respond to political pressure that has mounted as U.S. deaths have eclipsed 2,100. He and other administration officials are working to shore up slumping public support for the war in the run-up to the Dec. 15 vote in Iraq to create a democratically elected government that will run the country for the next four years.
While the president talked about reconstruction projects and the reopening of schools, markets and hospitals, the upgrading of roads and the growth of construction jobs in the two cities, he also acknowledged that challenges remain.
"Iraqis are beginning to see that a free life will be a better life," Mr. Bush said. "Reconstruction has not always gone as well as we had hoped, primarily because of the security challenges on the ground. Rebuilding a nation devastated by a dictator is a large undertaking."
Democrats were not impressed with the president's speech, reports CBS News correspondent Bob Fuss.
Rhode Island Democratic Sen. Jack Reed said Mr. Bush delivered more "vague generalities" without any real definition of what "winning" in Iraq entails.
"Again, I think the president owes the American people a much more detailed description of what he thinks success is," Reed said. "Complete victory is a nice slogan, but what does it mean and how long will it take?"
House Minority Leader Nancy Pelosi suggested that Mr. Bush was out of touch with reality in Iraq. "Just because he says thing are improving there, doesn't make it so," the California Democrat said.