Flight MS804 was travelling from Paris to Cairo with 66 passengers and crew when it vanished early on Thursday.
Greece's defence minister said radar showed the Airbus A320 had made two sharp turns and dropped more than 25,000ft before plunging into the sea.
Egypt says the plane was more likely to have been brought down by a terrorist act than a technical fault.
A major search operation involving Egyptian, Greek, French and British military units is taking place near the Greek island of Karpathos.
So far, no wreckage or debris from the aircraft has been found.
Flight MS804 left 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.
On the plane were 56 passengers, seven crew members and three security personnel.