Russia's ambassador to Nato, Dmitry Rogozin, said there could be no "consultations" with Georgia until Georgian forces returned to their positions and re-established "the status quo".
Accounts differ over who controls South Ossetia's capital, with Moscow saying it has "liberated" Tskhinvali.
In another development, separatists in Abkhazia - Georgia's other breakaway region - said they had launched air and artillery strikes on Georgian forces in the Kodori Gorge.
The crisis began spiralling when Georgian forces launched a surprise attack on Thursday night to regain control of South Ossetia, which has had de facto independence since the end of a civil war in 1992.
The move followed days of exchanges of heavy fire with the Russian-backed separatists.
In response to the Georgian crackdown, Moscow sent armoured units across the border into South Ossetia.
The BBC's Richard Galpin in Gori heard loud explosions and saw large plumes of smoke rising into the sky; soldiers and civilians were seen running through the streets.
Injured civilians were being pulled from the buildings, which were on fire.
The Georgian foreign ministry said the Black Sea port of Poti, the site of a major oil shipment facility, had been "devastated" by a Russian air raid.
Meanwhile Georgian TV reported that the Georgian-controlled section of the Kodori Gorge in Abkhazia was under fire, blaming the bombardment on Russian forces.
The foreign minister in Abkhazia's self-declared government, Sergei Shamba, said Abkhaz forces had launched an attack aimed at driving Georgian forces out of the gorge.
It was not clear whether planes used in the attack on the gorge belonged to Russia or to the Abkhaz separatists.
Russia has a peacekeeping force in Abkhazia under an agreement made following civil wars in the 1990s, when the region declared independence and formed links with Moscow.
President Medvedev said Russia's military aim in South Ossetia was to force the Georgians to stop fighting.
Russian minister defends action
"Our peacekeepers and the units attached to them are currently carrying out an operation to force the Georgian side to [agree to] peace," he said.
"They also bear the responsibility for protecting the population."
Speaking to the BBC, the Russian foreign minister insisted his country did not want all-out war with Georgia, but was prepared to do whatever was necessary to restore the situation in South Ossetia and to defend its civilian population, most of whom have been given Russian citizenship.
"Mr Saakashvili keeps saying that we want to chop off a part of Georgian territory," Mr Lavrov said.
SOUTH OSSETIA TIMELINE
1991-92 S Ossetia fights war to break away from newly independent Georgia; Russia enforces truce
2004 Mikhail Saakashvili elected Georgian president, promising to recover lost territories
2006 S Ossetians vote for independence in unofficial referendum
April 2008 Russia steps up ties with Abkhazia and South Ossetia
July 2008 Russia admits flying jets over S Ossetia; Russia and Georgia accuse each other of military build-up
7 August 2008 After escalating Georgian-Ossetian clashes, sides agree to ceasefire; however Georgia launches a surprise attack
8 August 2008 Russia sends in columns of armour and troops and fighting erupts with Georgian forces in and around Tskhinvali
9 August 2008 Russian jets bomb central Georgian town of Gori, Russia says its troops have "liberated" Tskhinvali
"He's also saying that this is not just about Georgia, this is about the future of Europe because he says Russia is also making territorial claims to other [countries], including the Baltic states, which is rubbish."
Mr Lavrov said Georgia had violated a peace deal under which Georgia had agreed not to use force in the South Ossetian dispute.
The BBC's James Rodgers in Moscow says diplomatic initiatives to end the fighting have so far proved fruitless.
On Friday evening, the UN Security Council failed to agree on the wording of a statement calling for a ceasefire.
The UK, the US and France, are pinpointing what they say is Russia's aggression as the key factor in the slide towards war, while Moscow insists Georgia is to blame.
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