Earlier, former interim Iraqi prime minister Iyad Allawi said the country was already in the grip of civil war, and Europe and the US would not be spared its consequences.
Mr Bush marked the anniversary without using the word "war", telling reporters he had been informed by US ambassador to Iraq Zalmay Khalilzad "of the progress the Iraqis are making toward forming a unity government" three months after national elections were held.
"We are implementing a strategy that will lead to victory in Iraq and a victory in Iraq will make this country more secure and will help lay the foundation of peace for generations to come," the president said on the White House lawn.
He is set to head to Cleveland, Ohio, later on Monday as part of his public relations campaign aimed at defending his Iraq strategy, where he will deliver a major speech.
Mr Bush did not refer to Mr Allawi's comments, however said he hopes Iraqis will soon form a unity government that "reflects the will of the people", and urged politicians to try harder.
"Civil war"
Mr Allawi told the BBC that the recent sectarian violence is a sure sign that the nation is embroiled in war.
"We are losing each day as an average 50 to 60 people throughout the country, if not more. If this is not civil war, then God knows what civil war is," he said.
"Iraq is in the middle of a crisis," he said, adding that he fears that sectarianism will spread not only throughout the region but even reach Europe and the United States.
Even members of Mr Bush's own Republican party have voiced their concerns over the mounting Iraqi death toll and the failure to reach agreement on a new government.
Top Republican, Senator Chuck Hagel, said US policy "needs new thinking".
"It's important that we stop this talk about we're not going to leave until we achieve victory," said Senator Hagel, speaking to America's ABC television.
He said Iraq has been in a "low-grade" civil war for as long as a year, and that the US has to stop talking about "victory" and think through responses to a worst-case scenario, like all-out civil war.
"Are we better off today than we were three years ago? Is the Middle East more stable than it was three years ago? Absolutely not," Senator Hagel said.
Australians troops should leave Iraq: poll
A survey of 500 Australians found two-thirds want Australian troops to return home now.
Thirty-two percent of respondents said the troops should remain there until Iraq is peaceful and stable.
In the US, opinion polls this week showed support among Americans for Mr Bush and the war have plunged to new lows.
Newsweek magazine's newest poll showed that approval of the president's handling of Iraq had plummeted to 29 percent while those who disapprove of his Iraq policy shot up to 65 percent.
A Wall Street Journal/NBC News poll put Mr Bush's overall approval ratings at 37 per cent.