TBILISI, GEORGIA - Vice President Dick Cheney assured Georgian leaders Thursday that the United States is "fully committed" to Georgia's pursuit of NATO membership, an assurance likely to further anger a Kremlin bent on keeping the Western military alliance out of former Soviet territory.

Meeting with Georgian President Mikhail Saakashvili in Tbilisi, Georgia's capital, Cheney used some of the harshest rhetoric yet from Washington against Russia, condemning its recent invasion and occupation of parts of Georgia as an "illegitimate, unilateral attempt" to forcibly change its tiny neighbor's borders.

"Russia's actions have cast grave doubts on Russia's intentions and on its reliability as an international partner," Cheney said.

Georgia was the second stop on a tour by Cheney of former Soviet republics. On Wednesday, he visited oil-rich Azerbaijan, and he wound up his day Thursday in Ukraine, which, like Georgia, wants to join NATO.

The vice president's trip was intended as a signal that the United States will continue cultivating close ties with Georgia and its neighbors even after Russia showed with its Aug. 7 invasion of Georgia that it was willing to use military force against countries along its border.

The Kremlin regards NATO's dialogue with Georgia and Ukraine about membership as a direct threat to its national security.

Russia has threatened to aim nuclear missiles at Ukraine if that country ever joins NATO, and many experts think Russia's underlying goal in invading Georgia was to undermine the Saakashvili government and nullify the country's chances of NATO membership.

"America will do its duty to work with the governments of Georgia and our other friends and allies to protect our common interests and to uphold our values," Cheney said while in Tbilisi.

The day before, the White House announced a $1 billion commitment in reconstruction and humanitarian aid to help Georgia recover from the Russian invasion.

Officials in Washington have been careful to emphasize that none of the assistance will involve aid aimed at reviving Georgia's military, which was heavily damaged by Russian forces during the brief war. The Kremlin has warned the West against rearming Georgia, and U.S. officials think any military assistance to Georgia now could again set off the tensions between Moscow and Tbilisi.

Saakashvili said Georgia was grateful for the new U.S. aid pledge, which matched his government's estimate of war damages. "Together with our other partners, in Europe, America and elsewhere, we will rebuild Georgia. We feel that we are not alone," he said.

Speaking in Moscow, Konstantin Kosachyov, head of the foreign affairs committee in the Kremlin-controlled lower house of parliament, accused Cheney of trying to forge an "anti-Russian axis."

"It's Cheney who was behind all recent events on the former Soviet turf," Kosachyov said in televised remarks.

The Associated Press and Washington Post contributed to this report.