The plane disappeared from radar two minutes after taking off from the resort of Sochi at 05:25 (02:25 GMT). Fuselage fragments have now been found and one body has been retrieved.
The defence ministry said the Tu-154 was carrying soldiers, 64 members of the famed Alexandrov military music ensemble, and nine reporters.
It was flying to Latakia in Syria.
The flight originated in Moscow and had 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)."
So far no survivors have been found.
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.
Reports from the area said flying conditions were favourable. An investigation into possible violations of safety regulations has been launched.
Mr Konashenkov said the plane was carrying passengers to a New Year's performance for Russian troops deployed in Syria.
The performance was scheduled to take place 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.
In April 2010, a Tu-154 plane crashed in Smolensk, western Russia, killing all 96 people on board, including Polish President Lech Kaczynski.
A Tu-154, operated by Siberian Airlines, was shot down over the Black Sea in October 2001, killing 78 people.
The plane was travelling from Tel Aviv in Israel to Novosibirsk in Russia, and most of the passengers were Israeli.
The Ukrainian military initially denied involvement but officials later admitted the plane could have been hit accidentally during a training exercise.