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Russian troops in the South Ossetian capital said their artillery had begun firing at Georgian forces, Russian news agencies reported.
Russia's president earlier promised to defend his citizens in South Ossetia.
Moscow's defence ministry said more than 10 of its peacekeeping troops in South Ossetia had been killed and 30 wounded in the Georgian offensive. At least 15 civilians are also reported dead.
Amid international calls for restraint, Georgia's president said 150 Russian tanks and other vehicles had entered South Ossetia.
Georgian President Mikhail Saakashvili says he is willing to agree an immediate ceasefire
He told CNN: "Russia is fighting a war with us in our own territory."