CAIRO (Reuters) - Egypt's Public Prosecutor has asked his French counterpart to hand over data on the crashed EgyptAir plane during its stay at Charles de Gaulle airport and until it left French airspace, his office said in a statement on Monday.

Nabil Sadek was requesting documents, audio and video records, it said. He has also asked Greek authorities to hand over transcripts of calls between the pilot and Greek air traffic control officials, and for the officials to be questioned over whether the pilot sent a distress signal.

EgyptAir flight 804 from Paris to Cairo vanished off radar screens early on Thursday as it entered Egyptian airspace over the Mediterranean. The 10 crew and 56 passengers included 30 Egyptian and 15 French nationals.

Ships and planes scouring the sea north of Alexandria have found body parts, personal belongings and debris from the Airbus 320, but are still trying to locate the "black box" recorders that could shed light on the cause of Thursday's crash.

French investigators say the plane sent a series of warnings indicating that smoke had been detected on board shortly before it disappeared.

The signals did not indicate what caused the smoke or fire, and aviation experts have not ruled out either deliberate sabotage or a technical fault.

Greek Defence Minister Panos Kammenos said on Friday that Greek radar had picked up sharp swings in the jet's trajectory as it plunged from a cruising altitude to 15,000 feet, then vanishing from radars. 

(Reporting by Haitham Ahmed; Writing by Ahmed Aboulenein; Editing by Andrew Roche)