Turkey announced that the Greek pilot died while the Turkish pilot ejected and was rescued by a Panama-registered cargo ship before being repatriated by a Turkish army helicopter
The two sides gave different accounts of the accident, which occurred about 55 kilometers (35 miles) south of the Greek island of Rhodes. The Turkish army said that the collision took place in international airspace and the Greek army said the planes were in airspace overseen by Athens.
Officials from the two countries said they would not let the incident affect bilateral relations, which have improved significantly in recent years.
The Turkish army said the two jets collided when Greek warplanes attempted to intercept Turkish jets on "routine training flights" in international air space.
The Greek armed forces, however, said the collision took place in the Athens Flight Information Region (FIR) - the flight zone overseen by the Athens airport control tower.
They said in a statement that a Turkish RF-4 and two F-16s entered the Athens FIR "without laying down flight plans" and heading towards the island of Crete, "violating the rules of aerial navigation".
Two Greek F-16s then took off to "investigate the planes and assure the security of international traffic", it said.
During a "reconnaissance manoeuvre", a Greek F-16 and a Turkish F-16 collided at an altitude of 8,230 metres (27,000 feet) and the planes crashed, the statement said.
Turkish Defence Minister Vecdi Gonul rejected the Greek statement.
"The incident took place in international airspace. Furthermore, our flight was a scheduled flight. It had been conveyed in advance to NATO," he told reporters in Ankara, the Anatolia news agency reported.
Turkey says its planes flying over the Aegean hand over flight plans to NATO before take-off and have posted their electronic in-flight identification since October 2001.
It says Greece does not reciprocate such measures.
Greek Foreign Minister Dora Bakoyannis and her Turkish counterpart Abdullah Gul spoke by telephone and expressed regret over the incident, saying it should not affect relations, the two foreign ministries said.
Despite a significant thaw in ties in recent years, Turkey and Greece remain at odds over territorial rights in the Aegean, accusing each other of violations.
Athens has long complained of frequent violations of its air space by Turkish aircraft. Turkey says its planes fly in international air space.
Greece claims a 10-mile air space limit around its coastline but Turkey only recognises six miles, arguing that under international rules Greece's airspace should be the same as its territorial waters.
Turkey is under European Union pressure to resolve territorial disputes with Greece, a bloc member.
In 1996, the two neighbours nearly went to war over an uninhabited rocky islet in the Aegean, but the United States stepped in and defused the tension.