Russian jets have been roaming Georgia's skies since Friday. They raided several air bases and bombed the Black Sea port city of Poti, which has a sizable oil shipment facility.
The Russian warplanes also struck near the Baku-Tbilisi-Ceyhan oil pipeline which carries Caspian crude to the West, but no supply interruptions have been reported.
Georgia President Mikhail Saakashvili called it an "unprovoked brutal Russian invasion."
A Russian raid on Gori near South Ossetia Saturday which apparently targeted a military base on the town's outskirts left numerous civilian casualties.
An Associated Press reporter who visited the town shortly after the strike saw several apartment buildings in ruins, some still on fire, and scores of dead bodies and bloodied civilians. The elderly, women and children were among the victims.
Russian officials said they weren't targeting civilians, but Russia's Foreign Minister Sergey Lavrov said that Georgia brought the airstrikes upon itself by bombing civilians and Russian peacekeepers in South Ossetia. He warned that the small Caucasus country should expect more attacks.
"Whatever side is used to bomb civilians and the positions of peacekeepers, this side is not safe and they should know this," Lavrov said.
Saakashvili on Saturday proposed a cease-fire, but Russia said it wants Georgia to first pull its troops from South Ossetia and sign a pledge not to use force against the breakaway province.
The diplomatic standoff continued Saturday in the UN Security Council, which met for the third time since late Thursday night to try to help resolve the situation. Another meeting requested by Georgia was scheduled for Sunday afternoon.
Georgia, a US ally whose troops have been trained by American soldiers, launched the major offensive to regain control over South Ossetia overnight Friday. Heavy rocket and artillery fire and air strikes pounded the provincial capital, Tskhinvali.
Lavrov told reporters Saturday that some 1,500 people had been killed in South Ossetia since Friday, with the death toll rising. The figures could not be independently confirmed.
But Tskhinvali residents who survived the bombardment by hiding in basements and later fled the city estimated that hundreds of civilians had died. They said bodies were lying everywhere.
Utiashvili, the Georgian Interior Ministry spokesman, said the Georgian troops were still in control of Tskhinvali on Sunday morning but added that Russian troops were attacking the city from several directions.
A Russian general said Saturday that his troops had driven the Georgian troops out of the city, but another Russian officer, Maj. Gen. Marat Kulakhmetov, admitted in televised remarks Sunday that the fighting in the city was continuing.
Alexander Lomaia, secretary of Georgia's Security Council, estimated that Russia sent 2,500 troops into Georgia. The Russian military would not comment on the number of troops.
In Saturday's meeting with refugees in the city of Vladikavkaz across the border, Prime Minister Vladimir Putin described Georgia's actions as "complete genocide. Putin also said Georgia had effectively lost the right to rule the breakaway province - an indication Moscow could be preparing to fulfill South Ossetians' wish to be absorbed into Russia.
Georgia's Foreign Ministry said the country was "in a state of war" and accused Russia of beginning a "massive military aggression." The Georgian parliament approved a state of martial law, mobilizing reservists and ordering government authorities to work round-the-clock.
Russia's President Dmitry Medvedev said that Moscow sent troops into South Ossetia to protect its peacekeepers and civilians on a mission to "enforce peace." He said that Russia would seek to bring the Georgian attackers to criminal responsibility.
Medvedev said he was ordering the military prosecutor to document crimes against civilians in South Ossetia.