EgyptAir Flight 804 from Paris to Cairo disappeared from radar over the Mediterranean Sea with 66 people on board early Thursday.
Greece Defence minister 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 (7,620m) before disappearing from radar, he added.
Egypt’s civil aviation minister has said the possibility of a terror attack is stronger than technical failure.
Of those on the plane, 56 were passengers, seven were crew members and three were security personnel.
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.
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 radar
Mr Kammenos said: “The picture we have at the moment on the accident as it emerges from the Greek air force operations centre is that the aircraft was approximately 10-15 miles inside the Egyptian FIR [flight information region] and at an altitude of 37,000 feet.
“It turned 90 degrees left and then a 360-degree turn toward the right, dropping from 37,000 to 15,000 feet and then it was lost at about 10,000 feet.”
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