Turkey has denied having a role in the crash that occurred off the Aegean island of Skyros.
A Greek fighter pilot died on Thursday when his plane crashed in the Aegean whilst returning from a mission to intercept Turkish jets, officials said.
"A Greek pilot [has entered] the pantheon of heroes," Defence Minister Panos Kammenos said in a tweet.
"He fell... fighting to defend national sovereignty and territorial integrity," he said.
A Greek general staff source told AFP that the Mirage 2000-5 plane was returning from a mission to intercept Turkish fighter jets.
"The mission was over and the plane was returning," the source said.
"We still don't know if there was an actual engagement with the Turkish airforce," the officer added.
Greece's state television channel ERT said the warplane disappeared shortly before it was due to land at an airfield on Skyros island in the central Aegean.
Greek fighter planes are regularly scrambled to intercept Turkish jets entering what Athens considers Greek airspace over the Aegean.
Turkey has denied having any role in the crash, saying there were no Turkish fighter jets in the area at the time of the incident, Turkish security sources told the state-owned Anadolu Agency.
The accident comes at a period of heightened tension between regional rivals and NATO allies Greece and Turkey.
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 accused Greece of failing to extradite eight former Turkish soldiers, who were part of an attempted 2016 coup, as well as members of the DHKP-C, an armed far-left organisation on the terror list of Turkey, the US and the EU.
In March, Turkey arrested two Greek soldiers who crossed the border illegally, allegedly whilst getting lost in the fog on patrol.