"A civilian aircraft crashed today and it is possible that it is the result of a terrorist act," Putin told a meeting of visiting European justice ministers.
Israel has suspended outgoing flights from Tel Aviv's Ben Gurion airport in the wake of the crash. Planes are still being allowed to land.
Mr Putin put the secretary of the country's Security Council in charge of an investigation into the crash.
An Armenian pilot in a nearby plane reported seeing an explosion on the Russian airliner before it crashed.
A Russian Emergencies Ministry spokesman said the plane - Flight 1812 - had gone down 185 kilometres (114 miles) off the Russian coastal town of Adler.
The water is understood to be about 90 metres (300 feet) deep at the scene of the crash.
Israel Airport Authority spokesman Pini Shif said air traffic controllers lost contact with the plane four hours into its flight.
He said there were no indications of any problems before the crash," so we have no information about what really happened".
Israeli aviation officials say Flight 1812 - a regular weekly charter flight - went through the same stringent security checks that are carried out on all planes travelling to or from the country.
Rescue effort
At least two bodies have been recovered from the sea by emergency rescue crews.
The Russian Emergencies Ministry said there were at least 66 passengers and 11 crew on board. About 50 of the passengers were recent immigrants to Israel from Russia, according to Israeli sources.
The plane crashed at approximately 1335 Moscow time (0935GMT), the agency said.
The three-engine TU-154 plane belonged to Siberia Airlines, which is based in Novosibirsk.
The BBC's Jonathan Charles says Russian airlines generally have a poorer safety record than their Western counterparts.
A TU-154 crashed in the eastern Russian city of Irkutsk in July, killing all 145 people on board.
That crash - the worst Russian air disaster in many years - was due to pilot error, an investigation concluded.