Greek and Turkish F-16 fighter jets have crashed into the southern Aegean Sea after colliding in mid-air.
The Greek pilot was killed, while the Turkish pilot was rescued after ejecting safely, Turkish officials say.
The collision, near Karpathos island, occurred after Greece scrambled a jet to intercept the Turkish aircraft, a Greek spokesman said.
Despite a thaw in recent years, the two neighbours have a long-standing territorial dispute over the Aegean.
Turkey insists Greek airspace extends only 10km (6 miles) offshore, not 16km (10 miles) as Greece maintains.
In the past, the two have come close to armed conflict over the dispute.
The incident occurred at about 27,000 ft (8,000 m), some 21 miles (34 km) southeast of Karpathos.
Greek government spokesman Evangelos Antonaros said the planes had gone down after touching wing tips.
"It was likely an interception operation," he said.
The BBC's Richard Galpin in Athens says interception attempts happen frequently, with the two sides shadowing each other and even staging mock dog fights in their disputed air space.
Nato has previously warned the two member states that these are dangerous.
The collision spotted by passengers on board a plane travelling to Cairo, according to eyewitnesses quoted on Greek television.
They reportedly saw an explosion in the sky.
The Turkish pilot survived and was repatriated by helicopter
The Turkish pilot was picked up by a passing merchant ship, Turkish officials said.
He was later flown home by an army helicopter. But the officials said the Greek pilot had died in the collision.
This has not been confirmed by the Greek government. However officials in Athens told the BBC they believe the pilot did not eject - and therefore may have died.
A search and rescue operation will continue for 72 hours, they said.
Turkish Foreign Minister Abdullah Gul conveyed his country's condolences to his Greek counterpart Dora Bakoyanni in a telephone conversation, the foreign ministry in Ankara said.
"The two foreign ministers expressed their regret at today's incident and agreed that this should not affect the two countries' efforts to improve their relations," a Greek foreign ministry statement said.
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