Officials with the airline and the Egyptian civil aviation department told Reuters they believed the Airbus A320 had crashed into the sea, Censor.NET reports
Egypt Air said the plane sent an emergency signal - possibly from an emergency beacon attached to the plane - at 04:26 a.m., two hours after it disappeared from radar screens.
In water crashes, an underwater locator beacon attached to the aircraft's flight recorders starts to emit a signal or ping. This helps the search and rescue teams to locate the boxes, and the location of the crash.
The aircraft was carrying 56 passengers, including one child and two infants, and 10 crew, EgyptAir said. They included 30 Egyptian and 15 French nationals, along with nationals from 10 other countries.
"The theory that the plane crashed and fell is now confirmed after the preliminary search and after it did not arrive at any of the nearby airports," said a senior aviation source, who declined to be identified.
"All causes for the disaster are open, whether it is a major technical fault or a terrorist action or any other circumstance. This will be ascertained when we inspect the plane's wreckage and transcribe its black boxes."
Families of passengers and the Egyptian prime minister rushed to Cairo International Airport shortly after dawn while the Egyptian and Greek military scrambled aircraft and boats to search for the plane.
The airline said on its Twitter account that Flight MS804, departed Paris at 23:09 (CEST). It disappeared at 02:30 a.m. at an altitude of 37,000 feet (11,280 meters) in Egyptian air space, some 280 kms (165 miles) from the Egyptian coastline, before it was due to land at 03:15 a.m., the airline said.