Georgia's Foreign Ministry said its soldiers were observing a cease-fire on orders of the president and declared the move in a note handed over to Russia's envoy to Tbilisi.
"Georgia expresses its readiness to immediately start negotiations with the Russian Federation on cease-fire and termination of hostilities," the ministry said in a statement.
A spokesman for the Russian Embassy confirmed the Georgian note was received; the Russian Foreign Ministry had no immediate response.
Georgia, whose troops have been trained by American soldiers, began an offensive to regain control over South Ossetia overnight Friday, launching heavy rocket and artillery fire and air strikes that pounded the provincial capital, Tskhinvali.
In response, Russia, which has granted passports to most South Ossetians, launched overwhelming artillery shelling and air attacks on Georgian troops.
Russia has demanded that Georgia pull out its troops from South Ossetia as a condition to negotiate a cease-fire. It also urged Georgia to sign a pledge not to use force against South Ossetia as another condition for ending hostilities.
Russia's Deputy Foreign Minister Grigory Karasin said that Moscow now needs to verify the Georgian withdrawal. "We must check all that. We don't trust the Georgian side," he said.
On Sunday, Russian jets raided a plant on the eastern outskirts of Tbilisi that builds Su-25 ground jets. The attack damaged runways but caused no casualties, said Georgia's Interior Ministry spokesman Shota Utiashvili.
"We heard a plane go over and then a big explosion," said Malkhaz Chachanidze, a 41-year old ceramics artist whose house is located just outside the fence of the factory, which has been running since the Soviet era. "It woke us up, everything shook."
The risk of the conflict setting off a wider war increased when Russian-supported separatists in another breakaway region of Georgia, Abkhazia, launched air and artillery strikes on Georgian troops to drive them out of a small part of the province they control. Fifteen U.N. military observers were told to evacuate.
Both South Ossetia and Abkhazia have run their own affairs without international recognition since splitting from Georgia in the early 1990s and have built up ties with Moscow. Russia has granted its passports to most of their residents.
In yet another sign that the conflict could widen, Ukraine warned Russia on Sunday it could bar Russian navy ships from returning to their base in the Crimea because of their deployment to Georgia's coast.
President Bush called for an end to the Russian bombings and an immediate halt to the violence.
"The attacks are occurring in regions of Georgia far from the zone of conflict in South Ossetia. They mark a dangerous escalation in the crisis," Bush said in a statement to reporters while attending the Olympic Games in Beijing.
Karasin said the ships were sent toward Abkhazia as a deterrent.
"The deployment is quite natural. We don't want a repeat of what happened in South Ossetia," he said at a news conference.
The foreign ministers of France and Finland were to arrive in Georgia Sunday to discuss ways to end the conflict.
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."
Jim Jeffrey, Bush's deputy national security adviser, warned "if the disproportionate and dangerous escalation on the Russian side continues, that this will have a significant long-term impact on U.S.-Russian relations."
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.
The U.N. Security Council planned to meet Sunday for the fourth time in four days to try to resolved the situation.
Karasin, Russia's deputy foreign minister, said more than 2,000 people had been killed in South Ossetia since Friday, most of them Ossetians with Russian passports. The figures could not be independently confirmed.
But residents of the provincial capital Tskhinvali 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.
Alexander Lomaia, Georgia's security council chief, estimated that Russia sent 2,500 troops into Georgia.
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 borders the Black Sea between Turkey and Russia and was ruled by Moscow for most of the two centuries preceding the breakup of the Soviet Union. Today, Russia has approximately 30 times more people than Georgia and 240 times the area.
Russia also laid much of the responsibility for ending the fighting on Washington, which has trained Georgian troops.
Washington, in turned, blamed Russia.
Georgia said it has shot down 10 Russian planes, including four brought down Saturday, according to Lomaia. It also claimed to have captured two Russian pilots, who were shown on Georgian television.
Russian Col. Gen. Anatoly Nogovitsyn, deputy chief of the General Staff, confirmed Saturday that two Russian planes had been shot down, but did not say where or when.
Russian military commanders said 15 peacekeepers have been killed and about 150 wounded in South Ossetia, accusing Georgian troops of killing and wounding Russian peacekeepers when they seized Russian checkpoints. The allegations couldn't be independently confirmed.
In Abkhazia, the separatist government said it intended to push Georgian forces out of the Kodori Gorge. The northern part of the gorge is the only area of Abkhazia that has remained under Georgian government control.
Separatist forces also were concentrating on the border with Georgia's Zugdidi region, and Russia's NTV television reported that additional Russian troops landed in Abkhazia Sunday, heading in the same direction.