Russia says Sunday's two explosions in its North Ossetia province, knocking out the main pipeline taking gas to Georgia, were the work of pro-Chechen insurgents.
But Georgian officials accuse Russia of deliberately triggering an energy crisis.
Georgy Arveladze, presidential chief of staff, said: "This morning, partial supplies of gas to Tbilisi resumed. It will take several days to resume gas supplies nationwide."
Georgia is getting additional gas from neighbouring Azerbaijan, which takes much of its gas via a separate pipeline from Russia.
Officials from Gazprom, the Russian gas monopoly, said the company was pumping an extra 2-3 million cubic metres a day to Azerbaijan for Georgia, where the winter is unusually harsh.
Georgia's relations with Moscow have been prickly since a pro-West government took power two years ago, with officials often accusing the Kremlin of meddling in the affairs of the country it once ruled.
Nino Burdzhanadze, the Georgian parliamentary speaker, told Russia's Ekho Moskvy radio that Sunday's attack: "Was a deliberate action against Georgia.
Georgia accuses Russia of delib-
erately sparking an energy crisis
"I am more than sure that major Russian forces, including special services, are unfortunately interested in destabilising the situation."
On Sunday, Mikhail Saakashvili, Georgia's president, called it "outrageous blackmail", likening it to a contract dispute earlier this year in which Russia cut off gas to another West-leaning neighbour, Ukraine.
Russian gas supplies to major customers in Western Europe fell, sparking concerns about a growing dependency on Russia for energy.
Ukraine officials have accused Russia of using its energy supplies to punish former Soviet states that are trying to integrate with the West.
On Monday, Gazprom again accused Ukraine of withholding natural gas supplies meant for delivery to customers in Europe and claimed that it was unable to fulfil all obligations to clients abroad as a result.
Russia is the world's largest gas producer and runs a close second to Saudi Arabia in oil exports.
Roland Nash, chief strategist at Renaissance Capital, wrote earlier this month: "Russia has established credibility that it is indeed willing to use energy for foreign policy initiatives.
"The Kremlin's determination to gain control over Russia's hydrocarbons has not simply been about access to revenue flows, but also to gain power that they are not afraid to use."
Moscow rejected Georgian accusations, warning the country's leadership that it was risking relations with Russia.
Russia says pro-Chechen rebels
were behind Sunday's attack
In a statement, the foreign ministry said: "Moscow is pretty much used to the behaviour of the Georgian government. What we see is a mixture of parasitic attitude, hypocrisy ... based on hopes to find Western patrons for their anti-Russian course.
"If Tbilisi has made up its mind to finally spoil relations with Russia, it must have calculated all consequences of such a policy."
The explosion came just after Georgian and Iranian talks about a possible gas pipeline to Armenia and on to Georgia. The United States is against the plan.
Georgia also has an agreement to buy gas, at a steep discount to world prices, from a pipeline running through its territory between Azerbaijan and Turkey and due to be completed towards the end of this year.
Analysts say that deal would greatly reduce Georgia's dependence on Russian gas.