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The plane disappeared from radar two minutes after taking off from Sochi at 05:25 (02:25 GMT), heading for Latakia in Syria.
Debris and several bodies have been found, with no reports of survivors.
The Tu-154 was carrying soldiers, reporters and 64 members of the famed Alexandrov military music ensemble who were to perform for Russian troops.
President Vladimir Putin has said Monday will be a day of national mourning.
The flight had originated in Moscow and landed at Adler airport in Sochi for refuelling.
The defence ministry said in a statement: "Fragments of the Tu-154 plane of the Russian defence ministry were found 1.5km (one mile) from the Black Sea coast of the city of Sochi at a depth of 50 to 70m (165-230ft)."
Ministry spokesman Maj-Gen Igor Konashenkov said: "No survivors have been spotted."

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The defence ministry has published a passenger list (in Russian), showing that 64 of those on board were from the Alexandrov Ensemble, including its director, Valery Khalilov.
There were nine journalists, eight soldiers, two civil servants and eight crew members.
Also on board was Elizaveta Glinka, known as Dr Liza, the executive director of the Fair Aid charity and the inaugural winner of Russia's state prize for achievements in human rights.
The Alexandrov Ensemble was scheduled to perform a New Year's concert at Russia's Hmeimim air base near Latakia.
Russia has been carrying out air strikes in support of Syrian government forces who are battling rebels opposed to Syrian President Bashar al-Assad.