Russia has resumed gas deliveries to neighbouring Georgia after supplies were cut by a series of unexplained explosions a week ago.
Many Georgians have been relying on bottled gas to stay warm
But while much of the capital, Tbilisi, was due to have gas on Sunday, it may take days for full service to resume across the freezing country.
Georgia had accused Moscow of sabotaging the pipes to put pressure on the pro-Western former Soviet republic.
Russia denied the charges outright, accusing Tbilisi of "hysteria".
As relations between the two countries deteriorated during the week, Georgia cut off gas supplies to the Russian embassy in the capital, saying it was more urgent to heat homes than buildings used by those taking part in an "energy blockade".
The crisis came during the coldest winter for decades, with temperatures plunging to as low as -20C.
"Russian gas has already crossed the Georgian border," Georgian Prime Minister Zurab Nogaideli told reporters on Sunday.
The crisis, he indicated, had brought home the fact that Georgia must end its near total dependence on Russian energy sources.
"The Georgian authorities will do everything so that our people are never again put in such a situation," he said. "Everyone saw clearly that Georgia cannot be broken."
Officials have already struck a deal with Iran to provide gas to ease the crisis, although that had not been expected to reach Georgia until Sunday night at the earliest.
Many Georgians have been trying to keep warm around makeshift wood-burning stoves, or queuing for hours to buy kerosene or bottled gas.
Russian officials have said "terrorists" were behind the blasts that damaged the pipes last Sunday, and angrily rejected charges by Georgia's president that it dragged its feet over making the necessary repairs.
But correspondents in Georgia say it is widely believed that Russia is simply punishing the country for its pro-Western course and its desire to join Nato and rid itself of the Russian military presence.
Relations between the two countries have been tense since President Mikheil Saakashvili was swept to power by the so-called "Rose Revolution" in 2003.
Concern has also been mounting within the international community over Russia's reliability as a supplier, after it cut supplies to Ukraine in the New Year over a row about prices.