Russia has warned Georgia it could take "retaliatory measures"
Nato has warned Russia that its recent troop build-up in Georgia's two breakaway regions undermines its neighbour's territorial integrity.
Russia's moves in Abkhazia and South Ossetia were raising tensions in the area, a Nato spokesman said.
Moscow has accused Georgia of preparing to invade Abkhazia, and says it is also boosting Russian peacekeeping forces there and in South Ossetia.
Tbilisi has described the Russian move as "irresponsible".
"The steps that have been taken [by Russia] and the rhetoric have increased tensions and undermined Georgia's territorial integrity," Nato spokesman James Appathurai said.
He also urged both Moscow and Tbilisi to avoid harsh rhetoric.
US National Security Council spokesman Gordon Johndroe on Wednesday said Washington was "concerned abut reports from the region".
The European Union has appealed for caution, saying to increase troop numbers would be unwise given current tensions.
Over recent weeks Russia appears to have been significantly turning up the pressure in Abkhazia and South Ossetia, the BBC's diplomatic correspondent Jonathan Marcus says.
He says that many Western diplomats see these moves as part of a more assertive Russian policy in the wake of Western recognition of the independence of Kosovo in February.
The row over Moscow's support for separatist enclaves in Georgia now threatens to provoke a more serious strain between Russia and the West, our correspondent adds.
Earlier this week, Russian Foreign Minister Sergei Lavrov warned that Moscow would take "retaliatory measures" if Georgia used force against its breakaway regions.
Georgia wants Russia to withdraw its troops from its two regions
Russia said Georgia was massing 1,500 soldiers and police in the upper Kodori Gorge, the only part of Abkhazia which remains under government control.
In response, Moscow said it was increasing Russian peacekeepers in both Abkhazia and South Ossetia.
Mr Lavrov said that Russia had to protect Russian-passport holders in the two regions.
Georgia denies any build-up of its own forces in the area, and says that Russia is taking provocative action.
"We think that this step, if they take it, will cause extreme destabilisation in the region," said Georgian Prime Minister Lado Gurgenidze.
"From now on, we consider every [Russian] soldier or any unit of military equipment coming in [to Abkhazia and South Ossetia] as illegal, potential aggressors and potential generators of destabilisation."
Russia has kept a peacekeeping force in Abkhazia and South Ossetia under an agreement made following the wars of the 1990s, when the regions broke away from Tbilisi and formed links with Moscow.
There are around 2,000 Russians posted in Abkhazia, and about 1,000 in South Ossetia.
Tensions between Russia and Georgia have flared up recently, despite Russia lifting economic sanctions against Georgia earlier this month.
Last week, Georgia accused a Russian plane of shooting down an unmanned Georgian spy plane - which Russian authorities insisted was shot down by Abkhaz rebels.
And on Tuesday, Georgia said it was blocking Russia's entry to the World Trade Organization.
Many in Abkhazia believe that Kosovo's announcement of independence from Serbia in February provides a precedent for it to be recognised as an individual state.
Although it has its own flag and postage stamps, it is not internationally recognised.