US President George W Bush spoke with Russian Prime Minister Vladimir Putin about the crisis while they attended the Beijing Olympics.
Later, the US voiced support for Georgia's territorial integrity and its state department said it would send an envoy to the region.
Nato said it was seriously concerned about the situation, while German Chancellor Angela Merkel called on all sides to show restraint.
The European security organisation, the OSCE, warned that the fighting risked escalating into a full-scale war.
Georgian Foreign Minister Ekaterine Tkeshelashvili told the BBC it wanted to ensure that any civilians who wanted to leave the conflict zone could do so safely.
International Red Cross spokeswoman Anna Nelson said it had received reports that hospitals in Tskhinvali were having trouble coping with the influx of casualties and ambulances were having trouble reaching the injured.
Georgian Prime Minister Lado Gurgenidze said Georgia had simply run out of patience with attacks by separatist militias in recent days and had had to move in to restore peace in South Ossetia.
Georgia accuses Russia of arming the separatists. Moscow denies the claim.
Russia earlier called an emergency meeting of the UN Security Council to respond to the crisis, but members failed to agree on a Russian statement calling on both sides to renounce the use of force.
The BBC's James Rodgers in Moscow says Russia has always said it supports the territorial integrity of Georgia but also that it would defend its citizens. Many South Ossetians hold Russian passports.
Hundreds of fighters from Russia and Georgia's other breakaway region of Abkhazia were reportedly heading to aid the separatist troops.
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