Bush's phone conversation with Dmitry Medvedev came after the U.S. leader called on Russia to stop bombing targets in Georgia, and voiced concern over the escalating violence.
Medvedev was quoted by the Kremlin as telling Bush: "Acting within our peacekeeping mission, and in line with the mandate issued by the international community, Russia is engaged in the task of forcing the Georgian side to accept peace, while defending the lives and property of its citizens, as is required under the Constitution and laws of the Russian Federation, and the legal standards of any civilized country.
Georgia, the main U.S. ally in the Caucasus Region, launched a major ground and air offensive to seize control of South Ossetia on Friday, prompting Russia to send in tanks and hundreds of troops. Georgia imposed martial law on Saturday after Russian warplanes began bombarding military bases.
Russia says 12 of its servicemen have been killed in the violence, and 2,000 civilians in South Ossetia have lost their lives. Around 30,000 refugees have flooded across the border into Russia to escape the violence since Friday morning.
A senior Russian diplomat said on Saturday that the country may ask the International Court of Justice and the European Court of Human Rights to investigate war crimes committed by Georgia.
"I do not rule out that the Hague and Strasbourg courts and institutions in other cities will be involved in investigating these crimes, and this inhuman drama that has been played out," Deputy Foreign Minister Grigory Karasin told news agencies in an interview broadcast on the Vesti-24 TV channel.
Russian peacekeepers "were killed by their own [Georgian] partners in the peacekeeping forces," he said.
"There is a Russian battalion, an Ossetian battalion, and a Georgian battalion... and all of a sudden the Georgians, Georgian peacekeepers, begin shooting their Russian colleagues. This is of course a war crime," Karasin said.
The ongoing conflict is the most severe since South Ossetia fought its way to independence from Georgia in 1992. The majority of the local population have Russian citizenship.
Georgian Interior Ministry spokesman Shota Utiashvili said earlier that Russian combat aircraft had bombed several Georgian military bases, one near the capital Tbilisi, as well as the Black Sea port city of Poti.
Georgian media also reported airstrikes on the city of Gori, and said several civilians had been killed.
However, Russian Deputy Air Force Commander Col. Gen. Anatoly Nogovitsyn denied that warplanes had struck non-military targets.
"We are not fighting peaceful towns, and are not conducting military strikes against civilians. We are only seeking to ensure peace," he said.
Georgia says it has shot down a total of 10 Russian combat aircraft, while Russia says it has lost two planes.
The Russian government has warned that a humanitarian disaster is developing as South Ossetians, many of them injured, flee across the border into Russia.
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The main event of the third day of the 11th meeting of the Valdai International Discussion Club in Sochi was the closing session with President Vladimir Putin. The atmosphere was calm and open, despite the current political tensions and the Russia-West confrontation. The Russian president said that it corresponded to the spirit of the Valdai Club.