Georgia has said its troops have pulled out of the breakaway region of South Ossetia and that Russian forces are in control of its capital, Tskhinvali.
But Russia said that while heavy artillery had been seen leaving the territory, Georgian troops were still present in other areas of the region.
Georgia's foreign ministry said it had ordered a ceasefire, and called for immediate talks with Russia.
The US has described Russia's actions as "dangerous and disproportionate".
US Deputy National Security Adviser James Jeffrey said that if the Russian escalation continued, it would have a "significant" long-term impact on relations between the Moscow and Washington.
"We're alarmed by this situation," he told reporters in Beijing.
Russian PM Vladimir Putin earlier suggested it was unlikely that South Ossetia would re-integrate with the rest of Georgia, saying the country's territorial integrity had "suffered a fatal blow".
Meanwhile, Russian warships were deployed off the Georgian Black Sea coast. Russia denied they were enforcing a blockade - saying they were simply searching ships for arms cargo - and said they later returned to port.
However, Ukraine threatened to block the return of Russian warships to their Black Sea base at Sevastopol saying it did not want to be "drawn into a military conflict".
Georgia says an additional 10,000 Russian soldiers have crossed into South Ossetia and Abkhazia. The separatist authorities in Abkhazia have announced full military mobilisation.
The BBC's Richard Galpin, who is on Georgia's crossing point into South Ossetia, says he has heard artillery fire between Georgian and Russian troops in the area.
Local residents fleeing the area told him there was continued fighting on the outskirts of the Tskhinvali, although the city itself was said to be relatively quiet with Russian forces in full control.
Earlier, Georgian officials said Russian jets had bombed a military airfield close to the Georgian capital, Tbilisi.
Three bombs had been dropped on the airfield, where there is a factory producing Sukhoi Su-25 fighter jets, they said.
There was no independent confirmation of the attack, although the BBC's Gabriel Gatehouse, who was in the city at the time, said he heard a loud explosion.
The current fighting began four days ago when Georgian forces launched a surprise attack 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 frontier.
"Georgia's aspiration to join Nato... is driven by its attempt to drag other nations and peoples into its bloody adventures" – Vladimir Putin
On Saturday, Georgian President Mikhail Saakashvili called for an immediate ceasefire after Russian planes carried out air strikes on the Georgian town of Gori, not far from South Ossetia. Scores of civilians were reported to have been killed.
The Georgian parliament has approved a presidential decree declaring a "state of war" for 15 days.
There are conflicting figures about the casualties suffered on both sides, and independent verification has not been possible, but the numbers appeared to rise sharply on Saturday.
Russian and South Ossetian estimates put the death toll on the South Ossetian side at more than 1,500, mostly civilians. Georgian casualty figures ranged from 82 dead, including 37 civilians, to a figure of about 130 dead.
Thousands of people are known to have fled into the neighbouring Russian region of North Ossetia and other parts of Georgia.
The UN High Commissioner for Refugees, Antonio Guterres, called for civilians trapped in conflict areas to be granted safe passage out.
Speaking to the BBC, Georgian interior ministry spokesman Shota Utiashvili said Georgian troops had pulled back to positions at or south of those held before 6 August, when the hostilities began.
From there, he said, they were engaged in fighting Russian forces.
ARMED FORCES COMPARED
Source: Jane's Sentinel Country Risk Assessments
Mr Utiashvili told the BBC that the withdrawal was necessary because of the mass civilian and military casualties both within South Ossetia and elsewhere in Georgia.
He said that Georgia was now facing a "humanitarian catastrophe", adding that 100 soldiers Georgian soldiers had been killed, and many more wounded.
A spokesman for the Russian military said Georgia had not withdrawn and insisted Georgia had to do that before any kind of ceasefire could come into effect.
A Russian commander in the conflict zone, Maj-Gen Marat Kulakhmetov, said the situation remained tense, and suggested both sides were preparing for further military action.
Earlier, Georgia said Russia had brought an additional 10,000 troops across Georgia's frontiers - 6,000 by land into South Ossetia and 4,000 by sea into Abkhazia.
The head of the pro-Russian separatist authorities in Abkhazia also said he had sent 1,000 troops to the Tbilisi-controlled Kodori gorge and announced the "full mobilisation" of reservists.
"We are ready to act independently," Sergei Bagapsh said. "We are ready to enforce order and go further if there is resistance from the Georgian side."
A Georgian interior ministry official later told the BBC that Russia had launched what he called "all-out military aggression" against Georgia, including attacking areas outside the conflict zone in South Ossetia.
He said Russian planes were now bombing the western town of Zugdidi and Georgian-controlled territory inside Abkhazia. The claims could not be independently verified.
The UN's Assistant Secretary-General for Peacekeeping, Edmond Mulet, said on Saturday that he feared the Abkhaz separatists were preparing to launch an offensive.
"At this point we are particularly concerned that the conflict appears to be spreading beyond South Ossetia into Abkhazia," he said.
Speaking on Saturday in the nearby city of Vladikavkaz, Mr Putin accused Georgia of seeking "bloody adventures" and trying to drag other countries into the conflict.
In an outspoken attack, he referred directly to Georgia's aspirations to join Nato, a move which Moscow strongly opposes.
Mr Putin described the actions of Georgian soldiers as genocide against the South Ossetian people and defended Moscow's military action to intervene directly.
Redrawing the map
Meanwhile, a joint delegation of the US, EU and the Organisation of Security and Co-operation in Europe is heading to Georgia in the hope of brokering a truce.
It comes as a third emergency session of the UN Security Council ended without an agreement on the wording of a statement calling for a ceasefire.
But emissaries from the US and Europe who are Nato members may not be seen as honest brokers by the Kremlin when it comes to Georgia, the BBC's diplomatic correspondent Bridget Kendall says.
The danger now is that Russia will not only use this crisis to demonstrate its military power in the region, but argue it is time to redraw the map, she adds.
Published: 2008/08/10 14:32:01 GMT