The plane disappeared from radar two minutes after taking off from Sochi at 05:25 (02:25 GMT), heading for Latakia in Syria, the defence ministry said.
Debris and 11 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.
More than 100 divers are involved in a round-the-clock search operation at the site of the crash, Russia’s defence ministry says.
Russia’s transport minister says investigators are looking into an “entire spectrum” of possible reasons the crash occurred, including the possibility of a terror attack.
Earlier, a Russian official had downplayed any suggestion of a terror attack.
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.”