"We are looking into this report," an Egyptian civil aviation ministry official told AFP. "At this point I can't deny or confirm it."
The Wall Street Journal, citing people familiar with the matter, said automated warning messages indicated smoke in the nose of the aircraft and an apparent problem with the flight control system.
The warnings, which were automatically sent by the Airbus A320's computer systems, came about 2:26 a.m. Thursday local time, just before air traffic controllers lost contact with the plane carrying 66 people, the Journal said.
The messages indicated intense smoke in the front portion of the plane, specifically the lavatory and the equipment compartment beneath the cockpit. The error warnings also indicated that the flight control computer malfunctioned, the report said.
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CNN also reported smoke alerts on the flight minutes before it crashed, citing information it obtained from an Egyptian source that was filed through the Aircraft Communications Addressing and Reporting System, which sends messages between planes and ground facilities.
Egypt's aviation minister has said a terrorist attack was a more likely cause than technical failure for the crash.
On Friday, search teams found wreckage including seats and luggage about 290 kilometers (180 miles) north of Egypt's coastal city of Alexandria, Egypt's military said.
The plane disappeared without any distress signal between the Greek island of Karpathos and the Egyptian coast.
It had turned sharply twice in Egyptian airspace before plunging 22,000 feet (6,700 meters) and vanishing from radar screens, Greek Defense Minister Panos Kammenos has said.