WASHINGTON (Reuters) - U.S. President George W. Bush left on Monday for his farewell NATO summit and a final heads-of-state meeting with Russia’s Vladimir Putin as he tries to salvage a foreign policy legacy frayed by the Iraq war.

President Bush gives a statement to the media alongside first lady Laura Bush, before their departure from the White House in Washington, March 31, 2008. REUTERS/Jason Reed

Seeking to reassert himself on the world stage in the twilight of his term, Bush will press NATO for more troops in Afghanistan, try to keep up momentum in the alliance’s eastward expansion and attempt to ease strains with Russia.

But with Bush even more unpopular overseas than at home, he could have a hard time swaying world leaders at this week’s Bucharest summit as they look to whomever will succeed him in January 2009.

“Many of them are looking forward now to the next president in Washington and are already thinking about what the 2009 summit will bring,” said Julianne Smith, a Europe analyst at Washington’s Center for Strategic and International Studies.

Lame-duck status will not be Bush’s only obstacle as he ventures abroad for the first in a series of international conferences marking his final year in office.

Overhanging his travels will be the 5-year-old Iraq war, which has damaged America’s credibility with friends and foes alike. The latest spike in fighting has increased doubts of further drawdowns of U.S. forces before Bush leaves office.

He will also be trailed by a financial crisis at home that has roiled global markets and sharpened criticism of his economic record, once seen as a bright spot of his legacy.

REASSURANCE FOR UKRAINE?

Bush’s first stop will be Ukraine, where he will try to reassure Kiev’s reform-minded government over its aspirations for NATO membership but offer no firm guarantees.

European partners are wary of letting Ukraine and Georgia into the alliance because of opposition from Moscow, which sees it as encroachment on the former Soviet sphere of influence.

Bush backs their bids for a roadmap for membership but may not have enough clout to overcome French and German misgivings at the April 2-4 summit in Bucharest.

Another source of friction is NATO’s role in the war in Afghanistan, which has led to transatlantic finger-pointing.

Bush wants a greater commitment from NATO partners reluctant to send troops to areas of heavy combat against a resurgent Taliban. A French offer of more forces has helped ease the dispute but it remains unresolved.

Bush’s national security adviser, Stephen Hadley, speaking to reporters aboard Air Force One en route to Ukraine on Monday, said it was “pretty clear” the NATO summit would produce a strong statement about Afghanistan.

“All of us need to do more in Afghanistan, and I think you’re going to see countries coming up and doing more,” Hadley said. He declined to say which countries would be doing more, saying the leaders should explain their own decisions.

Bush will share the summit spotlight with Putin, an unusual guest of the Western alliance. How the two leaders interact may signal whether the West’s relations with Russia will improve or deteriorate further.

Afterward, Bush will fly to Russia for a final round of one-on-one talks with Putin before he steps down as Russian president in May.

Slideshow ( 6 images )

The visit to Putin’s Black Sea villa in Sochi is aimed at using their personal chemistry to repair relations strained over missile defense, Kosovo independence and NATO expansion.

There has been speculation the two leaders will try to seal a compromise on a planned U.S. missile shield in Eastern Europe that Russia sees as a threat but which Washington insists is to deter countries like Iran that it considers “rogue states.”

Hadley said Bush and Putin might resolve some differences over missile defense as they work on a “strategic framework” for U.S.-Russian relations to bequeath to their successors.

“This is a complicated relationship,” he said. There were areas in which the two sides were trying to increase cooperation but also “areas where we disagree and we’re trying to manage those disagreements. That’s the framework in which we are moving forward.”

The talks could help Bush gauge how much power Putin will wield behind the scenes after Dmitry Medvedev, his protege, takes over as president and Putin becomes prime minister.

Bush famously said after his first meeting with Putin in 2001 that he trusted him after gaining a “sense of his soul.”

Critics say Bush was naive to believe Putin was committed to lasting democratic reform. Aides acknowledge Bush has become more realistic about Putin, who has grown more strident in his criticism of U.S. policies and more assertive of the former superpower’s place in world affairs.