The Airbus A320 passenger jet was flying at 37,000ft with 66 people on board when it disappeared on Thursday immediately after entering Egyptian airspace, EgyptAir said.
Greek authorities found "floating material" as well as life jackets in the southern Mediterranean Sea, Egypt's civil aviation ministry reported earlier.
Greek defence sources reported the discovery of two large plastic objects 80km south of Crete, just hours after flight MS804 travelling went missing.
"Prevailing northern winds of 20-50km per hour might have carried debris from MS804 that far during the day," Al Jazeera's John Psaropoulos reported from Athens citing officials.
"Egyptian authorities have undertaken the salvage operation."
EgyptAir said the plane disappeared from radar with 56 passengers and 10 crew members on board.
The airliner made "sudden swerves" mid-air and plunged before dropping off radars in the southern Mediterranean, Greece's defence minister said.
Sherif Fathi, Egypt's aviation minister, said the possibility of a "terrorist attack was stronger" than a technical failure.
No theories confirmed
French authorities have not confirmed any possible theories so far, Al Jazeera's Jacky Rowland reported from Paris.
"The French are not making a call on the Egyptian aviation minister's statements," she said.
"They are completely reserving judgement until more information is available."
An informed source at EgyptAir earlier said flight MS804, which departed from Paris' Charles De Gaulle Airport at 23:09 (CEST), was headed for Cairo when it disappeared from radar.
"At 4:26am, rescue teams affiliated with the Egyptian armed forces have received an SOS message from the emergency unit of the missing plane," EgyptAir said on Twitter.
The AFP news agency said the Egyptian army later denied detecting any distress signal from the missing airliner.
Source: Al Jazeera And Agencies