EgyptAir Flight MS804 from Paris to Cairo is believed lost some 130 nautical miles from the island of Karpathos, between Crete and Rhodes.
The pilot had spoken to Greek flight controllers some 25 minutes before the plane vanished from radar and had not reported a problem, the Greek civil aviation agency said.
"The flight controllers contacted the pilot (with the plane) at a height of 37,000 feet (near Athens)... he did not mention a problem," civil aviation chief Constantinos Litzerakos told Antenna TV.
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Litzerakos said the controllers had last spoken to the pilot "around 0005 GMT", some 25 minutes before the plane disappeared from Greek radar.
A civil aviation statement said the pilot "was in a good mood and gave thanks in Greek when authorized to exit the Athens flight information region.
"We tracked the entire process from the plane's entry (into Greek airspace) to its exit, it does not appear to deviate at all from the coordinates we gave," Litzerakos said.
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The Greek defence ministry said it had dispatched two search planes and a frigate to international waters in the area, with additional resources on standby on Karpathos and nearby Crete, including F-16 warplanes and a submarine.
Greece has asked France and other countries for satellite imagery that could provide additional clues, Kammenos said.
Twenty-six foreigners were among the 56 passengers, including 15 French citizens, a Briton and a Canadian, EgyptAir said.
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The company said contact was lost with the flight about 280 kilometres (175 miles) north of the Egyptian coast.
Neither the Greek coastguard nor the navy could confirm reports that a passing ship had seen "a ball of fire in the sky".
The civil aviation chief said if there had been an explosion, any debris would have scattered across a wide distance.
"It was at a height of 37,000 feet, dispersal is quite logical. This is quite an altitude," he told Antenna.