Earlier, Alexander Lomaia, the secretary of Georgia's security council, said that Russian forces had also occupied the Georgian city of Gori and that Georgian forces were fortifying positions near Tbilisi to defend the capital.
He said: "Russian forces are occupying Gori. Georgian armed forces received an order to leave Gori and to fortify positions near Mtskheta to defend the capital. This is a total onslaught."
Mtskheta is a Georgian city 24km from Tbilisi.
Moscow denied that it had taken Gori.
Earlier, Jonah Hull, Al Jazeera's correspondent outside Gori, confirmed that the city had been evacuated.
Hull said: "The evacuation began suddenly... when word came that the Russians were 5km to 10km from the city's limits. I have seen civilians and the army fleeing. Georgian troops clinging to the back of quad bikes. I have seen tanks leaving in no particular formation. It's panic basically."
Earlier on Monday, Mikheil Saakashvili, Georgia's president, spoke of the "cold-blooded, pre-meditated, murder" of his country and said that there would be "no surrender" to Russian aggression.
Appealing to the international community to step in to resolve fighting over the breakaway region of South Ossetia, he said: "The world has a moral duty to stop the madness."
Saakashvili made the comments at a news conference in Tbilisi, the Georgian capital, on Monday.
His remarks came as Russia's Interfax news agency said Georgian forces were continuing to shell Tskhinvali, the South Ossetian capital, early on Monday, killing three Russian peacekeepers and wounding 18 others.
Saakashvili said that the manner in which Russian troops mobilised in South Ossetia over recent days clearly indicated that it was a pre-meditated operation.
He said: "It is obvious... the Russian invasion had been planned for months and months and months. The timing of this intervention has been chosen deliberately [with regards] to the Olympics."
"It is so clear what has happened. We are in the process of invasion, occupation and annihilation of a democratic, independent country.
"Please wake up everybody and make your position and speak with a united voice... We are seeing the cold-blooded, pre-meditated, murder of a small country."
A cease-fire proposed by European Union envoys was signed in Tbilisi by Saakashvili on Monday morning, but Russia immediately rejected the document.
A Kremlin spokesman said: "According to information from peacekeepers in South Ossetia, Georgia continues to use military force and in this regard we cannot consider this document."
|Russia's deputy prime minister dismissed an EU cease-fire [AFP]
Sergei Ivanov, the Russian deputy prime minister, dismissed the EU efforts, saying the document was "not a ceasefire agreement".
Ivanov said a "cease-fire agreement is signed by two sides when they meet... we need a written agreement between Georgia on one side, South Ossetia and Abkhazia... that they will never use force in the future."
The document called for medical access to victims, a controlled withdrawal of troops on both sides and eventual political talks.
Meanwhile, Vladimir Putin, Russia's prime minister, said on Monday that the West had mistaken the real aggressors for the victims.
In a speech to senior government officials, Putin said some United States politicians still had a Cold War mentality.
"It is a shame that some of our partners are not helping us but, essentially, are hindering us," Putin said.
"I mean... the transfer by the United States of a Georgian contingent in Iraq with military transport planes practically to the conflict zone."
On Monday, the US military confirmed they had begun flying 2,000 Georgian troops home from Iraq after Georgia recalled them.
"The very scale of this cynicism is astonishing," said Putin.
"The attempt to turn white into black, black into white and to adeptly portray victims of aggression as aggressors and place the responsibility for the consequences of the aggression on the victims."
Earlier on Monday, Georgia's president said his country's existence was threatened by what he said was a Russian military onslaught centred on the breakaway region of South Ossetia but also including bombardments across Georgia.
At the weekend, Russian tanks attempted to advance in the direction of the town of Gori outside South Ossetia, but were turned back by Georgian forces.
Moscow officials have said that 2,000 people have been killed among the South Ossetian population, but Human Rights Watch (HRW), a New York-based rights group, said that appeared to be an exaggeration.
HRW also questioned Russia's claim that the conflict had resulted in 24,000 refugees, saying that refugees who had crossed the border multiple times may have been registered more than once.
Thousands of refugees have been housed in hostels in and around Vladikavkaz, the capital of North Ossetia, with others being sent to the cities of Nalchik, Krasnodar and Rostov in southern Russia.
"There are fears of propaganda and of disinformation. It's difficult to form an objective picture," said Tanya Lokshina, a HRW researcher.
Both South Ossetia and Abkhazia have run their own affairs without international recognition since fighting to break from Georgia in the early 1990s.
The two provinces have close ties with Moscow, while Georgia has deeply angered Russia by wanting to join Nato.