Interior Ministry spokesman Shota Utiashvili said the Vaziani military base on the outskirts of the Georgian capital was bombed by warplanes during the night and that bombs fell in the area of the Baku-Tbilisi-Ceyhan oil pipeline.
He also said two other Georgian military bases were hit and that warplanes bombed the Black Sea port city of Poti, which has a sizable oil shipment facility.
Utiashvili said there apparently were significant casualties and damage in the attacks, but that further details would not be known until the morning.
Russia dispatched an armored column into South Ossetia on Friday after Georgia, a staunch U.S. ally, launched a surprise offensive to crush separatists. Witnesses said hundreds of civilians were killed.
The fighting, which devastated the capital of Tskhinvali, threatened to ignite a wider war between Georgia and Russia, and escalate tensions between Moscow and Washington. Georgia said it was forced to launch the assault because of rebel attacks; the separatists alleged Georgia violated a cease-fire.
"I saw bodies lying on the streets, around ruined buildings, in cars," said Lyudmila Ostayeva, 50, who had fled with her family to Dzhava, a village near the border with Russia. "It's impossible to count them now. There is hardly a single building left undamaged."
The Interfax news agency cited the commander of Russian peacekeeping forces in South Ossetia, Marat Kulakhmetov, as saying Georgian artillery fired on Tskhinvali heavily early Saturday, but stopped around 2:30 a.m.
The fighting broke out as much of the world's attention was focused on the start of the Olympic Games and many leaders, including Russia's Prime Minister Vladimir Putin and U.S. President George W. Bush, were in Beijing.
The timing suggested Georgian President Mikhail Saakashvili may have been counting on surprise to fulfill his longtime pledge to wrest back control of South Ossetia - a key to his hold on power. The rebels seek to unite with North Ossetia, which is part of Russia.
Saakashvili agreed the timing was not coincidental, but accused Russia of being the aggressor. "Most decision makers have gone for the holidays," he told CNN. "Brilliant moment to attack a small country."
Diplomats issued a flurry of statements calling on both sides to halt the fighting and called for another emergency session of the United Nations Security Council, its second since early Friday morning seeking to prevent an all-out war.
"Since Russia is a veto-holding member of the U.N. Security Council, the negotiations were an attempt to keep Russia on board while the U.S. took a stand in support of the pro-Western government of Georgia and defended what it called Georgia's sovereignty and terroritorial integrity," said Falk, "but the fighting on the ground made an agreement difficult since neither Russia nor Georgia are a member of NATO."
U.S. Secretary of State Condoleezza Riceand withdraw combat forces from Georgian territory. Rice said in a statement the United States wants Russia to respect Georgian sovereignty and agree to international mediation.
CBS News correspondent Richard Roth reports that while Russia's plans remain unclear, both sides have strong political interests in keeping a lid on the violence. While Georgia hopes to join NATO, Russia would likely prefer to avoid conflict in a region so close to its own city of Sochi - slated to host the Winter Olympics in 2014.
The leader of South Ossetia's rebel government, Eduard Kokoity, said about 1,400 people were killed in the onslaught, the Interfax news agency reported. The toll could not be independently confirmed.
As night fell, there were conflicting claims as to who held the battlefield advantage.
Saakashvili said "Georgian military forces completely control all the territory of South Ossetia" except for a northern section adjacent to Russia. But Russian news agencies cited a Russian military official as saying heavy fighting was under way on the outskirts of the regional capital.
It was unclear what might persuade either side to stop shooting. Both claim the battle started after the other side violated a cease-fire that had been declared just hours earlier after a week of sporadic clashes.
The United States was sending in its top Caucasus envoy, Deputy Assistant Secretary of State Matthew Bryza, to try to end the bloodshed.
It was the worst outbreak of hostilities since the province won de facto independence in a war against Georgia that ended in 1992. Russian troops went in as peacekeepers but Georgia alleges they now back the separatists.
Russia, which has granted citizenship to most of the region's residents, appeared to lay much of the responsibility for ending the fighting on Washington.
In a telephone conversation with Rice, Russian Foreign Minister Sergey Lavrov said Georgia must be convinced to withdraw its forces, according to a ministry statement.
Georgia, which borders the Black Sea between Turkey and Russia, was ruled by Moscow for most of the two centuries preceding the breakup of the Soviet Union. Georgia has angered Russia by seeking NATO membership - a bid Moscow regards as part of a Western effort to weaken its influence in the region.
Saakashvili long has pledged to restore Tbilisi's rule over South Ossetia and another breakaway province, Abkhazia. Both regions have run their own affairs without international recognition since splitting from Georgia in the early 1990s and have built up ties with Moscow.
Georgia has about 2,000 troops in Iraq, making it the third-largest contributor to coalition forces after the U.S. and Britain. But Saakashvili told CNN the troops would be called home Saturday in the face of the South Ossetia fighting.
A senior U.S. defense official said Georgian authorities have asked the United States for help getting their troops out of Iraq. The official, who spoke on condition of anonymity because the discussions have been private, said no formal decision has been made on whether to support the departure, but said it is likely the U.S. will do so.
Also, Pentagon officials said Adm. Mike Mullen, chairman of the Joint Chiefs of Staff, has reached out to his counterparts in Russia and Georgia, but has not yet connected with them.
Georgia's Foreign Ministry accused Russian aircraft of bombing two military air bases inside Georgia, inflicting some casualties and destroying several military aircraft. Rustavi 2 television said four people were killed and five wounded at the Marneuli air base.
Twelve Russian troops were killed and 30 wounded in the fighting, said Russian Ground Forces spokesman Col. Igor Konashenkov. Saakashvili said late Friday that about 30 Georgians had been killed "mainly members of the Georgian armed forces."
Russia's Defense Ministry said it was sending in reinforcements for its troops in the province, and Russian state television and Georgian officials reported a convoy of tanks had crossed the border. The convoy was expected to reach the provincial capital, Tskhinvali, by evening, Channel One television said.
"We are facing Russian aggression," said Georgia's Security Council chief Kakha Lomaya. "They have sent in their troops and weapons and they are bombing our towns."
Putin warned in the early stages of the conflict that the Georgian attack would draw retaliation and the Defense Ministry pledged to protect South Ossetians, most of whom have Russian citizenship.
Chairing a session of his Security Council in the Kremlin, Russian President Dmitry Medvedev also vowed that Moscow will protect Russian citizens.
"In accordance with the constitution and federal law, I, as president of Russia, am obliged to protect lives and dignity of Russian citizens wherever they are located," Medvedev said. "We won't allow the death of our compatriots go unpunished."
On Friday, an AP reporter saw tanks and other heavy weapons concentrating on the Russian side of the border with South Ossetia supporting the reports of an incursion. Some villagers were fleeing into Russia.
Journalist Georgi Lomsadze witnessed the violence on the ground.
"People were very scared," Lomsadze told CBS News via phone. Some people [are] trapped right now. Many civilians [are] trapped in their houses, in their cellars as very heavy fighting still goes on."
Roads to the Russian border filled with refugees, reports CBS News correspondent Richard Roth.
The Georgian state minister for reintegration, Temur Yakobashvili, said Georgian forces had shot down four Russian combat planes over Georgian territory but gave no details. Russia's Defense Ministry denied an earlier Georgia report about one Russian plane downed and had no immediate comment on the latest claim.
Yakobashvili said one Russian plane had dropped a bomb on the Vaziani military base near the Georgian capital, but no one was hurt. More than 1,000 U.S. Marines and soldiers were at the base last month to teach combat skills to Georgian troops.
South Ossetia officials said Georgia attacked with aircraft, armor and heavy artillery. Georgian troops fired missiles at Tskhinvali, an official said, and many buildings were on fire.
Georgia's president said Russian aircraft bombed several Georgian villages and other civilian facilities.
A senior Russian diplomat in charge of the South Ossetian conflict, Yuri Popov, dismissed the Georgian claims of Russian bombings as misinformation, the RIA-Novosti news agency reported.
The Georgian attack came just hours after Saakashvili announced a unilateral cease-fire in a television broadcast late Thursday in which he also urged South Ossetian separatist leaders to enter talks on resolving the conflict.
Georgian officials later blamed South Ossetian separatists for thwarting the cease-fire by shelling Georgian villages in the area.