The US vice-president, Dick Cheney, yesterday issued a direct challenge to Moscow's sway over Georgia, pledging Washington's support for its eventual membership of Nato, while denouncing Russia's "illegitimate" invasion. "Georgia will be in our alliance," Cheney said after talks with President Mikheil Saakashvili.

Cheney used his one-day visit to Georgia to reinforce battle lines in the increasingly direct struggle between Washington and Moscow for the upper hand along Russia's southern border. His visit to Azerbaijan, Georgia and Ukraine was aimed at stressing America's "deep, abiding interest" in the region, in response to the claim by Russia's president, Dmitry Medvedev, that Moscow had "privileged interests" in former Soviet states.

The US challenge was undermined by the collapse of Ukraine's pro-western coalition on the eve of Cheney's arrival in Kiev at the end of his three-country trip yesterday. The crisis threatened to derail President Viktor Yushchenko's efforts to win Ukraine Nato and EU membership.

Cheney made clear however that it would not shake Washington's deep involvement in the region, now focused on Georgia after last month's conflict with Russia over South Ossetia.

Shrugging off Russian recognition of the breakaway republics of Abkhazia and South Ossetia, he declared the Bush administration's "strong commitment to Georgia's territorial integrity". The US would stand with Georgia, he said, "as you work to overcome an invasion of your sovereign territory and an illegitimate attempt to change your country's borders by force".

He also made a point of reaffirming US support for Saakashvili, who Moscow has derided as "a political corpse". In pointed contrast, Cheney told the Georgian leader: "You have been fearless in response to the occupation of your country and steadfast in your principles. We respect you."

The two men made a joint appearance near an aircraft factory destroyed by Russian bombing, to watch a US military transport plane unload blankets, part of the $1bn in emergency aid the US has offered Georgia to help the country rebuild. The package makes Georgia the biggest recipient of US aid after Israel, Egypt and Iraq.

US officials stressed the package did not include aid to rebuild Georgia's military. That will be decided later this year.

Georgian membership of Nato is due to be discussed at an alliance ministerial meeting in December. Russia insisted yesterday that such a move remained a red line in east-west relations. Dmitry Rogozin, Russia's representative to Nato, said Moscow would respond by halting co-operation with Nato over Afghanistan.

Cheney's trip coincided with the collapse of Ukraine's government after a split between Yushchenko and the prime minister, Yulia Tymoshenko. Their coalition collapsed over Russia's invasion of Georgia - with Tymoshenko positioning herself as a rival candidate to Yushchenko in Ukraine's presidential election next year. Yushchenko has lambasted Russia's occupation of Georgia, while Tymoshenko has refused to criticise the Kremlin directly.