Eyewitnesses said a large convoy of military vehicles carrying soldiers and towing heavy artillery was seen travelling south on Sunday through the village of Ergneti, south of Tskhinvali.
Grigory Karasin, Russia's deputy foreign minister, said 2,000, mostly Russian citizens, have died in South Ossetia since the fighting began.
Karasin said: "The results have been catastrophic. More than 2,000 people have died, most of them Ossetians, the majority Russian citizens."
He said if Georgia completely withdrew from South Ossetia then Moscow would be ready to negotiate with Tbilisi.
Meanwhile, the White House warned on Sunday that the war could have a "significant, long-term impact" on relations between Washington and Moscow.
James Jeffrey, deputy national security advisor, said Russia's reaction to the withdrawal of Georgian forces from South Ossetia would be key to future developments.
Speaking at a news conference on Sunday, Anatoly Nogovitsyn, deputy chief of the general staff of the Russian armed forces, said Russian peacekeeping forces were now in control of most of the capital.
Less than 25,000 armed personnel.
-19,000 troops in the Georgian army, around 2000 in the air force and 1,350 in the navy
It posseses Soviet-era fighter jets and a small fleet of second-hand naval vessels
More than one million permanent troops.
-395,000 army troops, besides 190,000 conscripts and 170,000 personnel in the air force
-It is estimated to have 1,700 fighter aircraft and 22,000 armoured vehicles
He said Georgia had not approached Russia regarding a request for a ceasefire.
The city has been ravaged by fierce battles since Friday, when Georgian troops launched an offensive to regain control over South Ossetia.
Russia responded by sending in tanks and troops and bombing Georgian territory.
The fighting is said to have left hundreds dead.
Georgia's interior ministry said that Russia has brought 6,000 troops into its territory and another 4,000 Russian troops are arriving by sea, allegedly preparing for an invasion on Sunday.
Earlier, Mikheil Saakashvili, the Georgian president, said his country is officially at war with Russia.
On Sunday, Georgia denied Russian media report that it had agreed with Russia to create "humanitarian corridors" to evacuate refugees from South Ossetia.
Shota Utiashvili, an interior ministry spokesman, said: "It's not true."
Earlier, the Organisation for Security and Cooperation in Europe had said it was working on creating conditions for the evacuation of refugees from the region after Georgia said it was withdrawing its forces from South Ossetia.
Russian air raid
Georgia has said that Russian planes bombed an airport attached to an aircraft manufacturing plant located 15km from Tbilisi, its capital.
A Georgian interior ministry spokesman said the attack inflicted some damage to its runways but caused no casualties.
While there has been no offical Russian response to the alleged bombing of the airport, Al Jazeera's Alan Fisher said injuries had occurred.
"Five people have been injured in what appears to be a Russian air raid," he said reporting from the scene.
"When you speak to people here, they have no idea why this place would be targeted, while there are military parts housed here, it is not a military base ... some say that perhaps there may have been confusion on the Russian side."
Inside Georgian territory, Russian jets carried out up to five raids targeting military installations around the town of Gori, about 30km outside South Ossetia, on Saturday.
Nogovitsyn said Georgia had shot down a Russian fighter jet and were holding the pilot.
Russian warships have set up a sea blockade of Georgia, Russia's Interfax news agency said on Sunday quoting a source in the Russian naval command.
"Our navy sailors have been assigned the task of preventing arms and other military supplies from reaching Georgia by sea," the source said.
Separately, RIA Novosti, another Russian news agency quoted a senior navy source as denying that a blockade was in effect.
"These reports do not correspond with reality. A coastal blockade would mean war with Georgia. We are not in a state of war with Georgia," the RIA Novosti source said.
Interfax also said that the Ukrainian foreign ministry had said that it reserved the right to bar Russian warships dispatched to the Georgian coast from returning to their Ukrainian base of Sevastopol.
"Ukraine... reserves the right to bar warships and vessels which could take part in the action (conflict with Georgia) from returning to Ukrainian territory until the conflict is solved," it said, quoting a Ukrainian foreign ministry statement.
Russia's Black Sea Fleet is based in the Ukrainian port.
Nogovitsyn said he could not comment on the Ukrainian statement.
South Ossetia deaths
A spokeswoman for South Ossetia's separatist government said on Sunday that at least 20 people were killed and 150 wounded by Georgian shelling overnight in Tskhinvali, the regional capital.
|A wounded South Ossetian soldier is pictured in the village of Dzhava [AFP]
Irina Gagloyeva said Georgian forces "fired on Tskhinvali methodically all night. But for now, a relative calm has settled in the city".
"The city is almost fully destroyed. Civilians left in the city are hiding in bomb shelters and basements," she said.
Meanwhile, the United Nations Security Council met for a third time on Saturday to discuss the situation.
Vitaly Churkin, Russia's ambassador to the UN, said a ceasefire "would not be a solution".
"The fighting is still going on. The Georgian forces are continuing to be on the South Ossetian territory," he said.
"The Georgian forces must pull out of South Ossetia.
"And then they must accept the need to sign an agreement on non-use of force with South Ossetians."
Fighting in Abkhazia
There was also fighting in Abkhazia, another breakaway region in western Georgia, where separatist forces say they had launched air and artillery strikes against Georgian troops.
Sergei Shamba, the de facto government's foreign minister, said Abkhazian forces intended to push Georgian troops out of the Kodori Gorge.
The northern part of the gorge is the only area of Abkhazia that has remained under Georgian government control. The region broke away from Tbilisi in the early 1990s along with South Ossetia.
Georgia's interior ministry on Sunday said that Russian aircraft had bombed a town in the region.
"Russian planes have not stopped bombing the Kodori Gorge since yesterday, and now they are also bombing Zugdidi," a Georgian town close to Abkhazia, an interior ministry spokesman said.
On Saturday, Georgian President Mikheil Saakashvili said Georgia had repelled several attacks in the area by Abkhaz separatists.
The head of Georgia's national security council said Sunday that Russian naval vessels had arrived in the Abkhaz port of Ochamchira.
Russia has yet to the comment on the claims that it attacked the Kodori Gorge or sent naval vessels to Abkhazia.