Egyptian Prime Minister Sherif Ismail said the search was underway to find the missing Airbus A320 and it was too early to rule out any explanation, including terrorism.
Officials with the airline and the Egyptian civil aviation department told Reuters they believed the jet had crashed into the Mediterranean between Greece and Egypt.
However, it remained unclear whether the disappearance was due to technical failure or any other reason such as sabotage by ultra-hardline Islamists, who have targeted airports, airliners and tourist sites in Europe, Egypt, Tunisia and other Middle Eastern countries over the past few years.
Egypt Air said the plane sent an emergency signal - possibly from an emergency beacon attached to the plane - at 04:26 a.m., two hours after it disappeared from radar screens.
In water crashes, an underwater beacon attached to the aircraft's flight recorders starts to emit a signal or ping. This helps search and rescue teams to locate the crash and find the boxes.
The aircraft was carrying 56 passengers - with one child and two infants among them - and 10 crew, EgyptAir said. They included 30 Egyptian and 15 French nationals, along with citizens of 10 other countries.
"The theory that the plane crashed and fell is now confirmed after the preliminary search and after it did not arrive at any of the nearby airports," said a senior aviation source, who declined to be identified.
Asked if he could rule out that terrorists were behind the incident, Prime Minister Ismail said: "We cannot exclude anything at this time or confirm anything. All the search operations must be concluded so we can know the cause."
"Search operations are ongoing at this time for the airplane in the area where it is believed to have lost contact," he told reporters at Cairo airport.
The pilot had clocked up 6,275 hours of flying experience, including 2,101 hours on the A320, while the first officer had 2,766 hours, the airline said.
Greek air traffic controllers spoke to the pilot as the jet flew over the island of Kea, in what was thought to be the last broadcast from the aircraft, and no problems were reported.
But just ahead of the handover to Cairo airspace, calls to the plane went unanswered, before it dropped off radars shortly after exiting Greek airspace, Kostas Litzerakis, the head of Greece's civil aviation department, told Reuters.