At a time when freezing winter temperatures are gripping all three countries, the explosions occurred on the main branch and a reserve branch of the Mozdok-Tbilisi pipeline close to the border with Georgia in the early hours of Sunday morning.
According to a spokesman for Russia's deputy prosecutor, general investigators at the site in the Russian province of North Ossetia, are treating the incident as sabotage, but not terrorism.
Sergei Prokopov, the spokesman, said: "An expert group is working at the site. According to preliminary information they have already found the remains of improvised explosive devices. If this explanation is confirmed then we are talking about sabotage."
Other officials said it could take up to four days to repair the damage due to the difficult mountain conditions.
Mikhail Saakashvili, the president of Georgia, accused Russia of being behind the blasts, which Georgia said could leave households without gas as soon as Sunday evening.
In a live television broadcast, Saakashvili said: "The explanation we have received from the Russian side is absolutely inadequate and contradictory ... Georgia has been subjected to serious sabotage from the side of the Russian Federation."
"We have long heard threats from Russian politicians that we could be left without light and gas ... and now this has happened, when Georgia is experiencing its coldest winter."
Aleko Khetagurov, Georgia's deputy energy minister, said a main electricity supply line from Russia had also failed around the same time as the gas pipeline explosions.
"The import of gas has been completely halted ... Talks are under way on supplies of gas from Azerbaijan and Iran, but this will take several days," Khetagurov said.
Georgia's relations with Moscow have been tense since Saakashvili was swept to power by a "rose revolution" in late 2003 and promised integration with the West, including a bid to join Nato.
"We have long heard threats from Russian politicians that we could be left without light and gas"
In his comments on Sunday, Saakashvili said the gas cut-off was linked to Russia's decision nearly to double the price it charges Georgia for natural gas from January 1.
Russia has significantly increased gas prices to several former Soviet republics that used to receive big discounts.