The Olympic flame, which was lit a week ago in Greece and flown to Moscow earlier Sunday, kept burning in a cauldron on Red Square.
The glitch occurred when a torch bearer ran through a long passageway leading into the Kremlin, which apparently created a wind tunnel, extinguishing the flame. A man standing along the route, most likely part of the presidential security service, pulled out a lighter and the flame leaped back to life.
Dmitry Chernyshenko, president of the Sochi organizing committee, said on Twitter that the problem was that the valve on the torch had not been opened fully.
The torch bearer, Shavarsh Karapetyan, 60, was a champion swimmer for the Soviet Union who once saved 20 passengers from a trolleybus that had fallen into a reservoir. He used his legs to break the back window of the trolleybus as it lay in 10 meters (30 feet) of water, and pulled out 20 of the 92 passengers.
The torch relay will stay in Moscow for the next three days, with hundreds of athletes, cultural figures and others, including Prince Albert II of Monaco, taking part.
The flame will then begin its journey across Russia, traveling from the western exclave of Kaliningrad to the easternmost point just across the Bering Strait from Alaska, before swinging back through the vast country to Sochi in time for the opening ceremony on Feb. 7.
For most of the 65,000- kilometer (39,000-mile) trip, the flame will travel by plane, train, car and even reindeer sleigh, safely encased inside a lantern. But 14,000 torch bearers also will take place in the relay at the more than 130 stops along the way.
One of the silver and red torches, unlit, will be carried into space in November for a brief visit to the International Space Station, and this same torch will be used to light the Olympic flame in Sochi.
Putin, for whom the Olympic Games are a source of personal pride, said the relay will "show the world Russia as she is and as we love her."
The torch relay will pass through many cities that showcase the historical, cultural and ethnic richness of Russia, while other cities on the route are more closely associated with the evils of Stalinism, the harsh treatment of dissent under Putin or the Islamic insurgency simmering in the Caucasus Mountains not far from Sochi's ski slopes.
As the relay crosses the expanses of Siberia, it will put the spotlight on Russia's immense wealth of natural resources and the rusting of its industrial towns.