Greek and Turkish F-16 fighters collided on Tuesday while shadowing each other over the southern Aegean, where the two Nato allies have long disputed control over airspace.
Greece and Turkey, which have come to the brink of war in the past over territorial disputes in the region, gave starkly differing accounts of the crash. But both hurried to limit damage to ties that have warmed markedly in the last six years.
Turkey's Foreign Ministry said it had "learnt with sadness that the Greek pilot lost his life". Athens announced search and rescue efforts were continuing and that he would be considered missing for at least 72 hours before being declared dead.
Greece said the Turkish pilot, flying one of three Turkish planes involved in the incident, had been rescued by a foreign commercial vessel and was later picked up by a Turkish military helicopter after refusing to board a Greek rescue helicopter.
Turkey said the crash was caused by a Greek fighter interfering in Turkish manoeuvres in international airspace.
Greece said two Greek fighters were scrambled after two Turkish F-16s and an RF-4 jet violated the Athens "flight information region", an area reaching out over the Aegean, heading towards the Greek island of Crete.
The collision occurred at about 27,000 feet (8,000 metres), some 21 miles (34 km) south-east of the island of Karpathos, whose mayor, Michalis Ioannidis, told Greek television islanders had heard an explosion but saw nothing.
MINISTERS, MILITARY TALK:
Turkish Foreign Minister Abdullah Gul called his Greek counterpart Dora Bakoyanni, who is visiting Helsinki, the Greek Foreign Ministry said in a statement.
"The two foreign ministers expressed their regret for today's incident and agreed that this should not affect the two countries' efforts to improve their relations," it said.
Turkish Defence Minister Vecdi Gonul said the Turkish and Greek military commanders had immediately contacted each other over the incident, the apparent fruit of confidence-building measures agreed last year to stop such incidents escalating.
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.
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.
"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 no major moves from Ankara on pending issues, including the Cyprus division.
A solution of territorial and air sovereignty disputes also eludes both countries.
Greece claims a 10-mile zone around its coast, but Turkey recognises only a six-mile zone. Turkey says it has the right to train in international airspace.
Athens says it daily scrambles fighters to intercept Turkish aircraft invading the airspace of its islands. Turkey denies the flights are a violation of Greek territory, saying it only flies in international airspace.
These manoeuvres, called "mock dogfights", can often involve very close high-speed approaches from both sides and draw formal protests from Ankara and Athens.