The Turkish Foreign Ministry claimed that the Greek pilot was killed in the incident while its own pilot ejected and was rescued by a Panama-registered cargo ship before being repatriated by a Turkish army helicopter.
Both Greece and Turkey are NATO members and allies but have also come to the brink of war in the past over territorial disputes in the region.
The two countries gave starkly differing accounts of the crash, but rushed to limit the political damage to ties that have warmed significantly in the last six years.
Athens announced search and rescue efforts were continuing and that the pilot would be considered missing for at least 72 hours before being declared dead.
Varying accounts
The incident occurred approximately 34 kilometres southeast of the island of Karpathos.
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 army denied the suggestion and said the planes were in airspace overseen by Athens.
The army said in a statement that a Turkish RF-4 and two F-16s entered the Athens flight information region "without laying down flight plans" and headed towards the island of Crete, "violating the rules of aerial navigation".
A formation of 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 27,000 feet (8,230 metres) and the planes crashed in the region, the statement said.
Turkish Defence Minister Vecdi Gonul denied the charges and said his country’s planes that were flying over the Aegean had handed over flight plans to NATO prior to take-off.
Turkey claims it has posted its electronic in-flight identification since October 2001 but that Greece does not reciprocate such measures.
Relations not strained by incident
Greek Foreign Minister Dora Bakoyannis and her Turkish counterpart Abdullah Gul spoke by telephone. They expressed regret over the incident and agreed that it should not affect relations.
"In their talks, the two ministers were unanimous on shedding light on the incident and not allowing it to affect bilateral ties," the Turkish foreign ministry statement said.
These measured and diplomatic exchanges are in stark contrast with the bitter rhetoric of the past, which highlights a dramatic improvement in ties between the two long-time rivals.
But analysts warn it could hamper further progress.
"This incident will not do any good," Thanos Veremis of the Hellenic Foundation for European and Foreign Policy think tank, told Reuters. "I think it will increase Greek frustration."
He said Greeks feel their moderation towards Turkey in recent years is not being reciprocated, with Ankara not making any major moves on pending issues.
The countries came close to war as recently as 1996 over a deserted Aegean outcrop and before that over the Mediterranean island of Cyprus in 1974 and 1963.
But ties have warmed in the last six years, with Greece backing Turkey's drive to join the European Union. Public opinion in both countries is however volatile.