Moscow is the main backer of Georgian separatists in the two enclaves of South Ossetia and Abkhazia, and has a "peacekeeping force" stationed in the region.
The Russian defence ministry said on Friday that ten of its peacekeepers had been killed and 30 injured in the fighting.
Russia's Interfax news agency reported that Eduard Kokoity, the South Ossetian separatist leader, had said that hundreds of civilians had been killed in the fighting.
Sergei Lavrov, Russia's foreign minister, said "ethnic cleansing" had been reported in villages in South Ossetia.
|Ossetian families try to escape the fighting [EPA]
He said: "We have heard about ethnic cleansing in villages in South Ossetia. The number of refugees is growing. A humanitarian crisis is looming."
Lavrov said the Georgian offensive had been made possible by Western military aid to Tbilisi.
"Now we see Georgia has found a use for these weapons and for the special forces that were trained with the help of international instructors.
"I think our European and American colleagues... should understand what is happening. And I hope very much that they will reach the right conclusions," he said.
In the US, the Pentagon said that it had been in contact with Georgian officials on Friday but had not had any request for assistance.
Mikhail Saakasvili, Georgia's president, said: "One hundred and fifty Russian tanks, armoured personnel carriers and other vehicles" had entered South Ossetia.
"This is a clear intrusion on another country's territory. We have Russian tanks on our territory, jets on our territory in broad daylight," Reuters new agency quoted him as saying.
"I must also tell you that Georgian forces have downed two Russian jet fighters over Georgia's territory."
Saakashvili said that most of the breakaway province of South Ossetia has been "liberated" in an overnight offensive.
He also said Russian aircraft bombed several Georgian villages and other civilian facilities, and that there were injuries and damage to buildings.
"Most of South Ossetia's territory is liberated and is controlled by Georgia," Saakashvili said in televised comments on Friday.
"[Russian] flights are ongoing in [over] the centre of Tskhinvali [the South Ossetian capital]... I demand Russia stop bombardment of peaceful Georgian cities."
Saakashvili's remarks came after Georgian tanks launched an attack on Tskhinvali on Friday.
|Georgian troops have surrounded Tskhinvali, the S Ossetian capital
Simultaneously, Georgian fighter jets attacked separatist positions in South Ossetia, Interfax
quoted the head of Russian forces in the region as saying.
Saakashvili said: "A full-scale aggression has been launched against Georgia [by Russia]. Georgia will not yield its territory or renounce its freedom," he said.
He also announced a full military mobilisation with reservists being called into action.
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."
Jonah Hull, reporting for Al Jazeera from the South Ossetian border with Georgia, said there had been a fairly sustained aerial bombardment of villages thought to be South Ossetian outposts.
Hull said: "The Georgian army used its superior firepower to overwhelming effect. Georgian tanks surged past Russian peacekeeping troops."
In televised remarks, Dmitry Medvedev, the Russian president, promised on Friday to defend Russian citizens in South Ossetia.
"Tonight in South Ossetia, Georgian forces bacically performed an act of aggression against Russiain peacekeepers and civilians.
|Medvedev said Georgia faced 'a deserved punishment' [EPA]
"What happened is a gross violation of international law and those mandates which were given at some point to Russia by the international community as a partner in conflict resolution.
"Now in South Ossetia, civilians, women, children and elderly are dying and the majority of them are Russian citizens.
"In accordance with the constitution and our federal laws as the president of the Russian Federation I am obliged to protect the life and dignity of Russian citizens wherever they are.
"The logic of the steps taken by us right now is dictated by these circumstances, we will not allow an unpunishable loss of lives of our citizens. The guilty will face a deserved punishment."
For his part, Vladimir Putin, the Russian prime minister, spoke of retaliation and pledged to protect Russian citizens.
Putin, on a trip to Beijing to attend the Olympics opening, did not specify the retaliatory action.
Most residents of South Ossetia and Abkhazia have Russian passports.
The European Union said on Friday it was "very concerned" at the escalation of violence, a European diplomat said.
"We are very concerned by the dramatic escalation of the situation," the diplomat told the AFP news agency.
Meanwhile, the United Nations Security Council failed to agree early on Friday on a statement drafted by Russia that would have called on Georgia and South Ossetia to immediately put down their arms.
"The Security Council is not yet in a position to express itself on the situation," Jan Grauls, the Belgian ambassador and the council president for August, said.
There were no immediate plans for the council to take up the matter again.
The council concluded it was at a stalemate after the US, Britain and some other members backed the Georgians in rejecting a phrase in the three-sentence draft statement that would have required both sides "to renounce the use of force", council diplomats said.