Speaking at the White House after a meeting with Tony Blair, the British prime minister, on Thursday, the US president said that remark, made in July 2003, was "kind of tough talk, you know, that sent the wrong message to people".
More than 2,400 Americans and many thousands of Iraqis have been killed in three years of war in Iraq and anti-American sentiment has increased across the Middle East and elsewhere.
Bush said: "I learned some lessons about expressing myself maybe in a little more sophisticated manner, you know. 'Wanted, dead or alive', that kind of talk. I think in certain parts of the world it was misinterpreted."
He also cited the Abu Ghraib prison abuse scandal as "the biggest mistake that's happened so far, at least from our country's involvement in Iraq".
"We've been paying for that for a long period of time," Bush said.
Blair said the effort to rid Iraq's army of members of Saddam Hussein's Baathists could have been done better.
"I think it's easy to go back over mistakes that we may have made," Blair said. "But the biggest reason why Iraq has been difficult is the determination by our opponents to defeat us. And I don't think we should be surprised at that."
Both leaders predicted difficulties ahead as the new government in Iraq tries to expand the influence of its security forces into more territory.
Blair is in Washington to brief
Bush on his recent Iraq visit
Blair said that "probably over the next few months there will be a real attempt by the anti-democratic forces to test them very, very strongly".
Bush said Baghdad needs a more effective police force and that General George Casey, his senior commander in Iraq, had met Nuri al-Maliki, the new prime minister, on Thursday to discuss how to improve security in the capital.
"It's really important that Baghdad, that the capital city, become more secure," Bush said.
Bush and Blair are under pressure from their respective electorates to show progress in Iraq so that they can start withdrawing their forces. There are about 132,000 American and 8,000 British troops there.
Blair, who recently visited Baghdad, said he believed that it was possible to meet al-Maliki's goal of having Iraqi security forces in control of all of Iraq by the end of next year.
"'Wanted, dead or alive', that kind of talk. I think in certain parts of the world it was misinterpreted"
Bush said: "Listen, I want our troops out - don't get me wrong. I understand what it means to have troops in harm's way ... But I also understand that it is vital that we do the job, that we complete the mission."
Blair said that "inevitably, over time, we have to transfer responsibility" because it will be easier for an Iraqi interior minister "who is the product of an Iraqi-elected government to go in and take the really tough measures sometimes that is necessary to sort some of these issues out".
As for now, he said: "This directly elected Iraqi government has said they want us to stay until the job is done."
In a plea to other countries, Blair said: "It is our duty, but it is also the duty of the whole international community to get behind this government and support it."