"Everything is developing according to plan," Sergei Shamba, the foreign minister of the de facto government in Abkhazia said on Vesti-24 television. He gave no information about casualties on either side.
The reported assault came after Russian forces moved into the towns of Senaki, Zugdidi and Kurga in western Georgia from Abkhazia on Monday.
Georgia also said that Russian forces had entered the Black Sea port city of Poti. Moscow described the move as a reconnaissance mission.
Alexander Lomaia, the secretary of Georgia's security council, said on Monday: "This is a total onslaught. Russian forces are occupying Gori.
"Georgian armed forces received an order to leave Gori and to fortify positions near Mtskheta to defend the capital."
Jonah Hull, Al Jazeera's correspondent, confirmed that the city of Gori had been largely evacuated.
"The evacuation began suddenly ... when word came that the Russians were 5km to 10km from the city's limits," Hull said.
"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.
"Basically, it's panic."
The UNHCR, the United Nation's refugee agency, said that 80 per cent of the 50,000 population of Gori had fled because of Russian attacks.
At least seven Georgian soldiers were injured in an attack on a military convoy leaving Gori, according to an AFP news agency photographer.
In South Ossetia, the separatist government said Georgia had resumed an artillery bombardment of its capital, Tskhinvali, where residents reported many deaths.
It has said 2,000 people have been killed in South Ossetia, a figure disputed by Georgia.
Meanwhile, Nicolas Sarkozy, president of France, which currently holds the rotating EU presidency, was due in Moscow on Tuesday to hold talks with Dmitry Medvedev, his Russian counterpart, on a plan to end the conflict.
But Russia's ambassador to the UN on Monday rejected the proposed Western draft resolution in the Security Council based on a three-point French peace plan.
|Up to 2,000 people have reportedly died in fighting in South Ossetia [AFP]
Bernard Kouchner, France's foreign minister, and Alexander Stubb, the foreign minister of Finland, which currently heads up the Organisation for Security and Co-operation in Europe, were also to push the peace plan to Russian officials.
Sarkozy was also expected to travel to Tbilisi later in the day to meet Saakashvili.
The diplomatic move came the day after George Bush, the US president, called for an immediate ceasefire saying he was "deeply concerned" that the Russians had moved "beyond the zone of conflict" and appeared to be moving to depose the Georgian president.
"Russia's government must respect Georgia's territorial integrity and sovereignty,'' the president said.
"[Its] actions this week have raised serious questions about its intentions in Georgia and the region."
But Vladimir Putin, Russia's prime minister, said on Monday that the West had mistaken the real aggressors for the victims.
"The very scale of this cynicism is astonishing," he said in a speech to senior officials.
"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."
An extraordinary Russia-Nato council meeting was also set to be held in Brussels on Tuesday at Moscow's request to discuss the conflict, according to an alliance spokeswoman.
The Georgian foreign ministry said on Monday that more than 50 Russian warplanes had flown over Georgian territory.
"Tbilisi was bombed. Bombs hit the village of Kojori and Makhata mountain," the ministry said in a statement.
Russia's military has acknowledged it had lost 18 soldiers and four aircraft in the conflict but gave no details of its latest operations.
Saakashvili said that "cold-blooded, premeditated murder" had been committed against his country and said that there would be "no surrender" to Russian aggression.
"The world has a moral duty to stop the madness," he said.
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.
"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," he said.
"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."