Georgia insists the breakaway regions are still its territory
Russia has accused the EU of signing a deal with Georgia on the deployment of ceasefire monitors that contradicts one agreed hours earlier with Moscow.
Russia's foreign minister said it would not permit EU monitors in South Ossetia or Abkhazia but that the deal signed by the EU with Georgia allowed this.
Georgia's breakaway regions have been recognised as independent by Russia.
The EU said it was not discussed with Moscow whether the observers could go into the separatist breakaway regions.
But EU foreign policy chief Javier Solana said he hoped EU monitors would eventually be deployed in any part of Georgian territory.
Russia agreed on Monday to pull its troops out of its self-declared buffer zones surrounding Abkhazia and South Ossetia. They had taken up position after the recent conflict with Georgia.
Russian President Dmitry Medvedev made the pledge on condition that at least 200 EU observers were deployed to ensure the security of the two breakaway regions.
Under the deal, Russia would pull out of Georgia proper within 10 days of the deployment of the EU monitors.
But Foreign Minister Sergei Lavrov said the EU was "ready to deploy monitors in the whole of Georgian territory".
He said such a move contradicted the deal signed by Mr Medvedev, which he said made clear that the EU monitors would only operate outside South Ossetia and Abkhazia.
Mr Lavrov described it as "a completely unscrupulous attempt" to mislead Georgian President Mikhail Saakashvili over the commitments given by the EU and Russia.
The Georgian president had cautiously welcomed Russia's agreement to withdraw its troops, calling it "a step forward".
However, he made it clear that he considered South Ossetia and Abkhazia inseparable parts of his country and said that the Russian military "should get the hell out".
Russia, however, said it would keep 7,600 troops in both disputed regions, and that it had established formal diplomatic ties with their administrations.
The move followed a decision - condemned by the US and EU but defined as "irrevocable" by Moscow - to recognise South Ossetia and Abkhazia as independent states.
Fighting between Russia and Georgia began on 7 August after the Georgian military tried to retake the breakaway region of South Ossetia by force.
Russian forces launched a counter-attack and the conflict ended with the ejection of Georgian troops from both South Ossetia and Abkhazia.