Egyptian Prime Minister Sherif Ismail said it was too early to say whether a technical problem or a terror attack caused the plane to crash.
"We cannot rule anything out," he told reporters at Cairo airport.
The Airbus A320 was flying at 37,000 feet when it disappeared shortly after entering Egyptian airspace at 2:45 am local time.
EgyptAir Flight 804 lost contact with radar after it entered Egyptian airspace, around 280 kilometres off the country's coastline north of the Mediterranean port city of Alexandria.
The "possibility that the plane crashed has been confirmed," the officials said.
EgyptAir said a "distress call" had been received from the plane two hours after it disappeared from radar. The Egyptian military, however, denied that any distress calls were received.
Egyptian military search and rescue teams were combing the area to locate the debris of the plane, which was carrying 56 passengers, including one child and two babies, and 10 crew members.
Apart from 30 Egyptians, the plane was carrying 15 French passengers, two Iraqis and one each from Britain, Belgium, Kuwait, Saudi Arabia, Sudan, Chad, Portugal, Algeria and Canada.
French Foreign Minister Jean-Marc Ayrault offered to send military planes and boats to join the Egyptian search for wreckage.
French President Francois Hollande held an emergency meeting and also spoke with Egyptian president Abdel-Fattah el-Sissi on the phone and agreed "to closely cooperate to establish as soon as possible the circumstances" surrounding the incident, according to a statement issued in Paris.
In March, another EgyptAir flight from Alexandria to Cairo was hijacked and forced to divert to Cyprus, where the hijacker demanded to see his former wife.
In October, the Islamic State jihadist group claimed responsibility for bombing a Russian airliner flying home holidaymakers from the Egyptian resort of Sharm El-Sheikh, killing all 224 people on board.
The group said it had smuggled a bomb concealed in a soda can on board the plane at Sharm El-Sheikh airport.
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