Russia's Emergency Ministry says there are no survivors in the crash of the Airbus 320 jetliner.
The aircraft was trying to land at the airport near the resort town, Sochi, when it crashed into the Black Sea, a few kilometers off shore.
More than a dozen boats are taking part in a search operation, which is being hindered by heavy rain. Officials say bad weather was the likely cause of the accident.
Rescue teams have recovered many bodies, as well as fragments of the fuselage, baggage and life jackets floating on the water.
A senior Emergency Situations Ministry official, Sergei Kudinov, says submersibles are also searching for wreckage, on the bottom of the sea.
Airport controllers say the plane disappeared from radar screens, shortly after 2:00 a.m.
A senior official with the Armenian national airline, Armavia, says the crash occurred as the pilot was making a second attempt to land the plane, in poor visibility.
The pilot had indicated he was returning to Armenia because of the conditions, but then turned to try landing again.
Sochi is a popular beach destination for people from the former Soviet Union, including Armenia.
Many of the passengers were en route to the resort ahead of the long holiday weekend which marks the end of World War II in Europe, May 9.