Russia says Georgian army’s shelling of main city is “open act of aggression”.
An earlier statement blamed the explosions on a car bomb.
The separatist government has previously accused Georgia of carrying out bomb attacks in the region – claims strongly denied by Tbilisi.
Tensions over South Ossetia and another breakaway Georgian region, Abkhazia, have soared in recent months, particularly since Moscow announced it was establishing formal ties with the separatists.
Unrest increased further this month with a series of bombings in Abkhazia, which the Abkhaz leadership blamed on Georgia.
Moscow’s admission that it had sent military jets on flights over South Ossetia has also fuelled tensions.