Last Updated: 5:57PM BST 08 Aug 2008
World leaders have appealed for a ceasefire in the conflict, which erupted after Georgia launched a huge offensive aimed at imposing its control over the rebel province with its large Russian population.
Separatist leaders in the South Ossetian capital Tskhinvali claim that more than a thousand people have been killed in Georgian shelling.
"We won't allow the death of our compatriots to go unpunished," Russian President Dmitry Medvedev said, adding that he would "protect the lives and dignity of Russian citizens wherever they are located".
Georgia claims that Russian aircraft have bombed two of its airbases, and that it has shot down five Russian jets.
President Mikheil Saakashvili of Georgia described the situation as "war". "Russia is fighting a war with us in our own territory," he said in an interview with CNN.
Moscow has denied sending aircraft into Georgian territory, but indicated that its forces have engaged with Georgian troops.
Sergei Lavrov, Russia's foreign minister, accused the Georgians of carrying out "ethnic cleansing" on the people of South Ossetia, most of whom have Russian passports.
The conflict threatens to draw in other world powers, with Mr Saakashvili considered a key ally of the West. The US has declared that it supports Georgia's "territorial integrity".
As a column of Russian tanks advanced towards Tskhinvali, Mr Lavrov called on the West to reach "the right conclusions" over the conflict, saying the Georgian offensive had been made possible by Western military aid to Tbilisi.
"Now we see Georgia has found a use for these weapons and for the special forces that were trained with the help of international instructors," he said.
"I think our European and American colleagues ... should understand what is happening. And I hope very much that they will reach the right conclusions."
The military operation marks the first time Russian troops have taken action on foreign soil since the Soviet withdrawal from Afghanistan in 1989.
Georgia has warned that any involvement of Russian forces in the conflict would result in a state of war between the two countries.
The Russian military reported that ten Russians were killed and 30 injured during Georgian shelling of their barracks, but Georgian officials denied firing on Russian peacekeepers in the area during their offensive in South Ossetia.
Georgia v Russia: By numbers
Georgia Russia: Population 4.6 million 140 million Army 18,000 400,000 Tanks 128 23,000 Fighter jets 9 1,736
The move by Russian troops followed a series of statements by Russian leaders pledging to protect Russian citizens in the region in the face of a massive Georgian military attack on South Ossetia.
Mr Putin, on a trip to Beijing to attend the Olympics opening, sharply criticised the Georgian attack and warned it will draw retaliatory actions. He spoke after meeting briefly with US President George W Bush in Beijing.
Mr Putin did not specify what kind of retaliatory action may follow, but Russia's Defence Ministry pledged to protect Russian citizens in the region. Most of the region's residents have Russian passports.
Russian President Dmitry Medvedev later chaired a session of his security council in the Kremlin, vowing that Moscow will protect Russian citizens.
"In accordance with the constitution and the federal law, I, as president of Russia, am obliged to protect the lives and dignity of Russian citizens wherever they are located," Mr Medvedev said in televised remarks. "We won't allow the death of our compatriots to go unpunished."
Russia's Defence Ministry denounced the Georgian attack as a "dirty adventure."
"Blood shed in South Ossetia will weigh on their conscience," the ministry said in a statement posted on its official website.
"We will protect our peacekeepers and Russian citizens," it said without elaboration.
Georgian President Mikhail Saakashvili accused Russia of aggression, saying that Russian jets bombed several Georgian villages, wounding seven civilians. A Russian diplomat denied that Russian aircraft had bombed Georgian territory.