The mayor of Aegean island Skyros, Miltos Hatziyiannakis, told state-run Greek television station ERT that men in a fishing boat found "some of the remains of the plane" and the pilot's body on Thursday evening.

The death of 34-year-old father of two Georgios Baltadoros comes at a period of heightened tension between Greece and Turkey.

It prompted Turkish Prime Minister Binali Yildirim to call his Greek counterpart Alexis Tsipras on Thursday, during which the two leaders pledged to "strengthen dialogue" between the regional rivals and NATO allies.

Baltadoros' Mirage 2000-5 plane fell into the sea a short distance from Skyros airport as it returned from a mission to intercept Turkish jets that had entered what Greece considers its airspace.

The Turkish planes had already left by the time Baltadoros and a wingman arrived in the area near the island of Lesbos, in the eastern Aegean.

The cause of the crash is being investigated.

Greek media have speculated that the pilot suffered a blackout or spatial disorientation.

The condition of his body indicates that "he was unable to react" to the crash, Hatziyiannakis said.

Greece's armed forces are observing a three-day mourning period for the pilot.

Greek fighter planes are regularly scrambled to intercept Turkish jets entering airspace over the Aegean, occasionally engaging in mock dogfights.

Earlier this week, Greek soldiers fired warning shots at a Turkish helicopter after it approached the small island of Ro, which is on Greece's border in the southeastern Aegean Sea.

Turkish President Recep Tayyip Erdogan and members of his government have escalated verbal attacks on Greece after its failure to extradite eight Turkish soldiers that Ankara said were part of an attempted 2016 coup.

In March, Turkey captured and is still holding two Greek soldiers who crossed the border, allegedly while getting lost in the fog on patrol.

burs-jph/dl