Separatists, who have controlled the region since the early 1990s, vowed to repel the attack without calling for help from Russia, their main backer.
In a sign of broadening conflict, hundreds of volunteers from Russia and Georgia's other breakaway region of Abkhazia headed to South Ossetia to support the separatist forces, Russian news agencies reported.
"It is not too late to avert massive bloodshed and new victims," the Russian foreign ministry said in a late-night statement.
"We hope our foreign partners will remain impartial in this difficult moment, when the fate of hundreds of thousands people is decided," it said. "The Georgian leadership should ... return to civilised ways of solving complicated problems."
Temur Iakobashvili, Georgia's reintegration minister, confirmed that "Tskhinvali is surrounded by Georgian forces", adding that government forces had taken control of five Ossetian villages loyal to separatists.
Mikheil Saakashvili, Georgia's president, had on Thursday offered an immediate halt to heavy fighting, after a week of clashes in which nearly 20 people were killed.
"Let's stop this spiral of violence ... let's resume negotiations," he had said in his televised address.
Saakashvili also reiterated a previous offer of "practically limitless" autonomy for South Ossetia and proposed that Russia could be the guarantor for any deal.
Officials from the two sides had been due to hold peace talks at a Russian peacekeeping base on Friday and Russian peacekeepers in the region reported that shelling had stopped for at least four hours after Saakashvili's televised speech.
But Georgia then accused separatists of shelling its villages and launched a large-scale military operation.
"We are forced to restore constitutional order in the whole region," General Mamuka Kurashvili, the head of Georgian peacekeepers in the region, said in comments broadcast on Georgia's Rustavi-2 television network.
"Despite our call for peace and a unilateral ceasefire, separatists continued the shelling of Georgian villages," he said.
Martin McCauley, a London-based Russia analyst, told Al Jazeera: "You can argue that the president of South Ossetia, who wants independence from Georgia, is deliberately provoking Tbilisi and is trying to suck Russia in."
South Ossetia and Abkhazia, receive extensive political and financial backing from Moscow.
Tbilisi has repeatedly accused Russian peacekeepers of supporting the separatists, while Moscow has accused Georgia of planning a full-scale invasion to re-establish control over the region.
"Russia is responsible for what is happening now in the conflict zone. Because it's not us who supply the arms for the separatists," Georgia's Iakobashvili said.
But Grigory Karasin, Russia's deputy foreign minister, on Thursday dismissed Georgian claims that Russia was responsible for the fighting as "cynical and unfair".
"The responsibility for the new outbreak of tensions in the region rests upon the Georgian side,'' he said.
"We have to remind them again that it is impossible to resolve the South Ossetian problem with military methods."