CAIRO —Greek and Egyptian authorities diverged Monday on what happened to EgyptAir Flight 804 during the crucial final minutes before it crashed into the Mediterranean, killing all 66 people on board.

A French ship joined the international effort to hunt for the black boxes and other wreckage of the jetliner, searching for clues to what brought the plane down.

Five days after the air disaster, questions remain over what happened to the jet before it disappeared off radar about 2:45 a.m. local time Thursday.

Egyptian authorities said they believe terrorism is a more likely explanation than equipment failure, and some aviation experts have said the erratic flight reported by the Greek defense minister suggests a bomb blast or a struggle in the cockpit. But so far no hard evidence has emerged.

A 2013 report by the Egyptian ministry of civil aviation records that the same Airbus 320 made an emergency landing in Cairo that year, shortly after taking off on its way to Istanbul, when one of the engines overheated. Aviation experts have said that overheating is uncommon yet is highly unlikely to cause a crash.

The head of Egypt’s state-run provider of air navigation services, Ehab Azmy said the plane did not swerve or lose altitude before it disappeared off radar, challenging an earlier account by Greece’s defense minister.

Azmy, head of the National Air Navigation Services Company, said that in the minutes before the plane disappeared it was flying at its normal altitude of 37,000 feet, according to the radar reading. ‘‘That fact degrades what the Greeks are saying about the aircraft suddenly losing altitude before it vanished from radar,’’ he added.

According to Greece’s defense minister Panos Kammenos the plane swerved wildly and dropped to 10,000 feet before it fell off radar.

Forensice experts were carrying out DNA tests on some of the human remains that have been recovered.