An EgyptAir flight from Paris to Cairo made two sharp turns before plunging into the Mediterranean Sea, Greece's defence minister says.
Panos Kammenos said the Airbus A320 had "turned 90 degrees left and then a 360-degree turn to the right".
It then dropped more than 25,000ft before disappearing from radar, he added.
Egypt's civil aviation minister has said the possibility of a terror attack is "stronger" than technical failure.
Sherif Fathi added that no wreckage had yet been found but latest reports suggest search teams have sighted debris from the plane.
Sixty-six people were on board, most of them from Egypt or France.
The search in seas south of the Greek island of Karpathos involves Greek and Egyptian naval forces.
Of those on the plane, 56 were passengers, seven were crew members and three were security personnel. A Briton was among those on board.
Flight MS804 left Charles de Gaulle airport in Paris at 23:09 local time on Wednesday (21:09 GMT) and was scheduled to arrive in the Egyptian capital soon after 03:15 local time on Thursday.
EgyptAir said the plane had been flying at 11,300m (37,000ft) when it disappeared from radar shortly after entering Egyptian airspace.
Greek aviation officials say air traffic controllers spoke to the pilot when he entered Greek airspace and everything appeared normal.
They tried to contact him again at 02:27 Cairo time, as the plane was set to enter Egyptian airspace, but "despite repeated calls, the aircraft did not respond". Two minutes later it vanished from radarFrench President Francois Hollande said he was keeping an open mind about the cause: "We will draw conclusions when we have the truth about what happened.
"Whether it was an accident, or whether it was - and it's something that is on our minds - terrorism."
Far too early to say: By Richard Westcott, BBC transport correspondent
An Egyptian aircraft disappearing without a mayday is bound to raise the spectre of terrorism.
But the truth is it is far too early to say why this plane vanished.
Whatever happened, it happened too quickly for the crew to raise the alarm.
Initially, the aircraft seemed to drop off the radar at 37,000 feet, suggesting a sudden break-up. It is very rare for modern planes to simply break apart in mid-air. That meant an explosion was a real possibility.
But then the Greek defence minister described the aircraft making sharp turns and dropping height quickly, which suggests it was intact for longer.
Even in the worst emergencies, pilots tell me they should have time to call for help, once they have got to grips with the problem. But not always.
Some of the relatives of those on board gathered at airports in Cairo and Paris to wait for news.
French Foreign Minister Jean-Marc Ayrault who met some of the relatives at a crisis centre in Paris Charles de Gaulle called it a "moment of intense emotion" for them
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