Russian troops have been in control of the port of Poti
Russia has told Nato it is halting all military co-operation, the bloc says, as the crisis over Georgia deepens.
The Russian move follows a statement by Nato that there would be no "business as usual" with Moscow unless its troops pulled out of Georgia.
However, the alliance had stopped short of freezing co-operation with Moscow.
Meanwhile, a top Russian general said that the withdrawal of the bulk of Russia's troops would be complete in about 10 days.
Gen Vladimir Boldyrev, commander of the Russian ground forces in the region, referred to the pullout of troops "sent to reinforce Russian peacekeepers" in Georgia's breakaway region of South Ossetia.
It was not immediately clear how Gen Boldyrev's comments would fit in with a previous Russian commitment to withdraw its forces to behind a buffer zone around South Ossetia by the end of Friday.
Russia needs co-operation with Nato no more than Nato needs Russia
Russian Foreign Minister Sergei Lavrov
Moscow has said it intends to keep some 500 troops in what it called a "zone of responsibility" as part of a peacekeeping mission.
In a separate development, South Ossetia and Abkhazia - another Georgian breakaway region - held mass rallies calling for independence.
Russian Foreign Minister Sergei Lavrov said Moscow's response to their pleas would depend on the conduct of Georgian President Mikhail Saakashvili.
Nato spokeswoman Carmen Romero said the alliance "takes note" of Russia's decision to halt co-operation but had no further reaction to it.
Speaking to reporters in the Russian Black Sea resort of Sochi, Mr Lavrov said Russia was not going "shut any doors" to future co-operation with Nato.
But he warned that the alliance had to decide what was more important to it - supporting Mr Saakashvili or developing a partnership with Russia.
Latest footage of Russian troops near Igoeti in Georgia.
"It all depends not on us but on those who make the decisions on what the priorities are for the leaders of Nato in foreign policy," Mr Lavrov said.
Washington played down the significance of the Russian move, saying Nato had already effectively frozen co-operation in protests at Moscow's continuing military presence in Georgia.
"For all practical purposes, military-to-military co-operation had really already ended with the Russians," US National Security Council spokesman Gordon Johndroe said.
Under the 2002 agreement that set up the Nato-Russia Council, the former adversaries began several co-operation projects.
These included allowing Nato to transport by land through Russia non-military supplies for the bloc's operation in Afghanistan, developing battlefield anti-missile technology, joint military exercises and help with rescue at sea.
It is still not clear to what extent Russian military forces have withdrawn from Georgia.
Russian news agencies say an armoured column, consisting of more than 40 vehicles, has passed through South Ossetia, on its way to the Russian border.
A BBC correspondent in the Georgian village of Igoeti, just 35km (21 miles) from the capital Tbilisi, said he saw the Russian military pulling back towards South Ossetia early on Thursday afternoon.
Russian forces were also reported to be still dug in around Georgia's main Black Sea port of Poti.
Russia poured troops into Georgia after Georgian forces tried to retake South Ossetia on 7 August. Russian-led peacekeeping troops had been deployed there since a war in the early 1990s.
Thousands of people attended pro-independence rallies in the Abkhaz capital Sukhumi and war-ravaged South Ossetian capital Tskhinvali on Thursday.
Gergiev conducted Tchaikovsky and Shostakovich symphonies
The world-renowned conductor Valery Gergiev, himself an Ossetian, gave a concert in the devastated South Ossetian capital Tskhinvali with his home orchestra, the Mariinsky of St Petersburg.
Gergiev, who is also principal conductor of the London Symphony Orchestra, performed a requiem of Russian music for a city he compared in a speech to Stalingrad.
As the orchestra performed with South Ossetia's shattered parliament building as a backdrop, soldiers and civilians listened side by side.
Gergiev told his audience - and the world - that Georgia, not Russia had been the aggressor. "We know how much people suffered," he said in English.
"We know how much these children suffered, old people. Let's not allow it to happen ever again. And I want to say if it was not for the help from the Russian army there would be more casualties, more victims - thousands and thousands more."
The chain of events is deeply contested, the BBC's Sarah Rainsford reports, but what is certain is that the Ossetians clutching candles and soaking up this music amid the ruins of Tskhinvali now have no desire to reunite their breakaway region with Georgia.
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