Nine journalists were among the passengers, with state-run channels Pervy Kanal, NTV and Zvezda saying they each had three staff onboard the flight.
There were also eight crew members onboard, 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.
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 airbase, agencies reported.
'Too early'
Kremlin spokesman Dmitry Peskov told news agencies 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.
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.