"Unfortunately, we believe that no one managed to survive," Irina Andriyanova, Russia's emergency situations ministry spokeswoman, said.
Forty-five children and 10 crew members were among the dead, according to the deputy head of St Petersburg-based Pulkovo airlines which operated the aircraft.
The airliner was flying from the Black Sea resort of Anapa to Saint Petersburg when it disappeared from radar screens after issuing an SOS, the emergency ministry said.
The wreckage of the Tupolev Tu-154 has been found about 45km north of Donestk.
Russian authorities said they had ruled out terrorism.
"The plane most likely was hit by lightning," Andriyanova said in televised comments. "After it fell, it broke apart and burst into flames."
Another Russian aviation official said the aeroplane might have run into strong turbulence, the Interfax news agency reported.
Igor Krol, a spokeman for the Ukrainian emergencies ministry, said that a fire had broken out in the plane at an altitude of 10,000 metres. The crew had then decided to make an emergency landing.
A Tupolev Tu-154 (file)
Anatoly Simushin, Pulkovo Airlines deputy director, said the pilot sent four distress signals as he tried to climb above the storm, then descended to an exceptionally low altitude of 3,000 metres before crashing.
The 16-year-old aircraft had flown 9,000km since its last maintenance check, airline officials said.