At the opening of a NATO summit, Mr. Bush also urged allies to increase their forces in Afghanistan to confront a strengthening Taliban insurgency.
On the eve of his visit to Jordan for meetings with Iraqi Prime Minister Nouri al-Maliki, Mr. Bush portrayed the battles in both Afghanistan and Iraq as central fronts in a war "against the extremists who desire safe havens and are willing to kill innocents anywhere to achieve their objectives."
The stakes in Iraq are huge for President Bush. His war policies were repudiated in U.S. midterm elections that handed control of Congress to Democrats. A bipartisan blue-ribbon panel is about to issue a report proposing changes in the administration's approach in Iraq. And al-Maliki's government itself sometimes seems to be at cross purposes with Washington.
Mr. Bush set the stage for the Jordan talks with a speech at the NATO summit here and at an earlier news conference in neighboring Estonia. The president said he was flexible and eager to hear al-Maliki's ideas on how to ease the violence.
"There's one thing I'm not going to do, I'm not going to pull our troops off the battlefield before the mission is complete," President Bush declared in his speech. There are about 140,000 U.S. forces in Iraq.
Meanwhile, the U.N. Security Council voted unanimously to extend the mandate of the 160,000-strong multinational force in Iraq for one year, acting quickly ahead of a key meeting between U.S. and Iraqi leaders aimed at halting escalating violence in the country and paving the way for a reduction of American troops.
The council responded to a request from al-Maliki, who said a top government priority is to assume full responsibility for security and stability throughout the country but that it needs more time.
Earlier, speaking with reporters in Tallinn during a joint news conference with Estonia's president, Mr. Bush would not debate whether Iraq had and blamed the increasing bloodshed on a pattern of sectarian violence that he said was set in motion last winter by al Qaeda followers.
"I'm going to bring this subject up, of course, with Prime Minister Maliki," Mr. Bush said. "My questions to him will be: What do you need to do to succeed? What is your strategy in dealing with the sectarian violence?"
But senior administration officials say that when Mr. Bush sits down with al-Maliki tomorrow, it is al-Maliki who might push for troop withdrawals so Iraqis can take greater control of their own security, CBS News chief White House correspondent Jim Axelrod reports.
The president said he realized that "no question it's dangerous there, and violent. And the Maliki government is going to have to deal with that violence, and we want to help them do so."
Mr. Bush has been coming under increasing pressure, both overseas and at home, to reach out more to other countries.
Such a recommendation may be among those issued by the Iraq Study Group headed by former Secretary of State James A. Baker III and former Democratic Rep. Lee Hamilton. The group is expected to finish its work next month, and some are hoping for it by early next week. The Bush administration rejected what is expected to be a key recommendation — engaging Iran and Syria for help calming Iraq, Axelrod reports.
CBS News national security correspondent David Martin reports that sources close to the Iraq Study Group predicted that its final report will not call for a timetable for a withdrawal of troops — something that would certainly be rejected by the administration.