Minister Ahmet Davutoglu said Friday's incident was inexcusable and he has requested a NATO meeting to discuss a response, the BBC said.
That meeting is scheduled for Tuesday. The Turks have also consulted with the United Nations and European Union, the report said.
Davutoglu said the F-4 Phantom jet was in international airspace when it was shot down over the Mediterranean Sea after briefly straying into Syrian territory at high speed on a training mission, CNN reported.
"You have to first send a caution, a warning," he said. "If the warning doesn't work, you scramble your planes, you send a stronger signal, you force the plane to land. There wasn't enough time to do any of that in the time that our plane was in Syrian airspace."
The Turkish navy was searching Sunday for the two pilots who went down in the burning jet, although their chances of survival were considered slim, the reports said.
The wreckage of the jet was located Sunday afternoon at a depth of 3,000 feet, although the aviators weren't found, Russia's RIA Novosti news agency reported.
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