A US warship arrived on Thursday in Georgia's port of Batumi, the US embassy said, sending a message of support to NATO allies amid the spiralling crisis in neighbouring Ukraine.

The USS Taylor's "presence in Georgia reaffirms the United States' commitment to strengthening ties with NATO allies and partners like Georgia, while working toward mutual goals of promoting peace and stability in the region," the embassy said in a statement.

The US 6th Fleet frigate arrived in Georgia for three days of exercises with the country's coastguard in the Black Sea after completing joint live-fire exercises and an anti-submarine warfare scenario along with Romanian ships.

"Allied ships, planes, exercises show vigilance and resolve from the Baltic to the Black Sea. We'll keep reinforcing NATO security," NATO Secretary General Anders Fogh Rasmussen wrote on Twitter on Wednesday.

Events in neighbouring Ukraine's standoff with Russia have alarmed Tbilisi which fought and lost its own war with Moscow in 2008, and says it is still exposed to a Russian threat.

Still no sign of Russian troop pullback from Ukraine border: NATO
Warsaw (AFP) May 08, 2014 - NATO said Thursday it had yet to see "any indications" that Russia has withdrawn its troops from the Ukraine border, a day after President Vladimir Putin claimed to have done so.

"Let me assure you that if we get visible evidence that they are actually pulling back their troops, I will be the very first to welcome it," NATO Secretary General Anders Fogh Rasmussen said in Warsaw.

"I have to repeat that while we have noticed the Russian statements that they have started to withdraw troops, so far we haven't seen any, any indications that they're pulling back," he said after talks with Polish Prime Minister Donald Tusk.

US and NATO officials estimate Russia massed 40,000 troops on the border with Ukraine as the Kiev government battles pro-Kremlin militias.

Putin announced a pullback on Wednesday in response to Western concerns of a possible Ukraine invasion, but both the Western military alliance and the United States have questioned the claim.

"For those with a blind eye we suggest to follow President Putin's statement of May 7," Russia's foreign ministry said on Twitter after Rasmussen tweeted that he saw no sign of a withdrawal.

Asked about the Russian tweet by reporters in Warsaw, Rasmussen responded: "I have very good vision."

Rasmussen follows up his two-day visit to Poland by heading Thursday to Baltic state Estonia, where he will lead a delegation of the North Atlantic Council, NATO's main political decision-making body.

The 28 members of the North Atlantic Treaty Organisation have responded to Russia's intervention in Ukraine by stepping up defences in Eastern Europe, sending warships, fighter jets and troops to the region.

The troop surge is scheduled to end on December 31, but the alliance has said the build-up could become permanent.