Mr Bush has 10 months left in office
US President George W Bush is set to offer backing to Ukraine's membership of Nato as he starts a visit to the former Soviet republic.
The eastward expansion of the military alliance has divided Nato members due to fierce opposition from Moscow.
Mr Bush will go on to attend his final Nato summit in Bucharest, Romania, at which troop commitments to Afghanistan are likely to be discussed.
He will then hold a last summit with Russian President Vladimir Putin.
Mr Putin is leaving office in May, while Mr Bush's term ends next January.
The trip is being seen by some commentators as a last bid by Mr Bush to score some successes in foreign policy, when his legacy abroad has been tarnished by the ongoing fallout of the US-led invasion of Iraq in 2003.
'Eager to talk'
Mr Bush arrived in the Ukrainian capital Kiev late on Monday at the start of a two-day visit.
Ukraine protesters railed against both Mr Bush and Nato membership
He will seek to convince sceptics in Nato that Ukraine should be welcomed as a member, said the US ambassador to Kiev, William Taylor. "President Bush is also eager to talk himself with these leaders [in Ukraine] and with other people in this city so that he can go to Bucharest with even stronger arguments," he said.
European partners in Nato have been guarded about Ukrainian and Georgian ambitions to join in the face of heated opposition from Russia - including a threat to train nuclear weapons on Ukraine.
After Kiev, Mr Bush will travel to Bucharest for a Nato summit on Wednesday, and then stop in Croatia for two days, before travelling to Russia's Black Sea resort of Sochi for what are likely to be his final talks with Mr Putin.
About 1,000 protesters gathered in Kiev waving anti-Bush posters - some obscene - ahead of the president's visit, the Associated Press reports.