The plane had been on a routine flight to Russia's Hmeimim air base in western Syria.
A Russian military plane crashed on its way to Syria on Sunday, with no sign of survivors among the 92 onboard, who included dozens of Red Army Choir members heading to celebrate the New Year with troops.
The Tu-154 plane went down in the Black Sea shortly after taking off from the southern city of Adler where it had been refuelling, defence ministry spokesman Igor Konashenkov said in a briefing broadcast on the ministry's website.
It disappeared from radar just two minutes after it took off at 5:25 am (0225 GMT).
The ministry told agencies there was no sign of any survivors at the crash site and that 10 bodies had been recovered off the coast of the resort city of Sochi, as authorities pledged to dispatch more than 100 divers to aid in the search.
"Fragments of the Tu-154 plane of the Russian defence ministry were found 1.5 kilometres (0.9 miles) from the Black Sea coast of the city of Sochi at a depth of 50 to 70 metres (165 to 230 feet)," the ministry said.
President Vladimir Putin told state television that Russia will observe a national day of mourning on Monday.
The plane had been on a routine flight to Russia's Hmeimim air base in western Syria, which has been used to launch air strikes in Moscow's military campaign supporting its ally President Bashar al-Assad in the country's devastating civil war.
Among the plane's 84 passengers were Russian servicemen as well as 64 members of the Alexandrov Ensemble, the army's official musical group also known as the Red Army Choir, and its conductor Valery Khalilov. They were headed to Syria to participate in New Year celebrations at the air base.
The passengers also included nine journalists, with state-run channels Pervy Kanal, NTV and Zvezda saying they each had three staff onboard the flight.
There were also eight crew members, the ministry said.
A list of passengers published by the defence ministry also included Elizaveta Glinka, a doctor and charity worker who serves on the Kremlin human rights council.
Probing cause of crash
Mikhail Fedotov, who heads the council, said Glinka was travelling to Syria to bring medication to a university hospital in the coastal city of Latakia near the air base, agencies reported.
Assad, as well as German Chancellor Angela Merkel, Turkish Prime Minister Binali Yildirim and the US Embassy in Moscow, expressed condolences over the crash.
Kremlin spokesman Dmitry Peskov said that Putin was being kept updated on the search operation and was in constant contact with Defence Minister Sergei Shoigu.
Konashenkov said that deputy defence minister Pavel Popov had flown to Adler along with a team tasked with clarifying the circumstances surrounding the crash.
Transportation Minister Maxim Sokolov, who is heading a state commission probing the crash, is also on his way to the region, the government said in a statement.
The ministry has not put forward any possible causes of the crash.
Konashenkov said that the aircraft had been in service since 1983 and had flown some 7,000 hours since. The plane last underwent repairs in December 2014 and was serviced in September, he said.
Russia's Investigative Committee said a criminal probe had been launched to determine whether violations of air transportation safety had led to the crash.
Investigators are currently questioning the technical personnel responsible for preparing the plane for take-off, the committee said.
Tu-154 aircraft have been involved in a number of accidents in the past.
In April 2010 many high-ranking Polish officials, including then president Lech Kaczynski, were killed when a Tu-154 airliner went down in thick fog while approaching Smolensk airport in western Russia.
Moscow has been conducting a bombing campaign in Syria in support of Assad since September 2015 and has taken steps to boost its presence in the country.
In October, Putin approved a law ratifying Moscow's deal with Damascus to deploy its forces in the country indefinitely, firming up Russia's long-term presence in Syria.
Russian warplanes have flown out of the Hmeimim base to conduct air strikes, and the base is also home to an S-400 air defence system.