Turkish fighter jets shot down a Russian warplane near the Syrian border on Tuesday after repeated warnings over air space violations, but Moscow said it could prove the jet had not left Syrian air space.

It was the first time a NATO member's armed forces have downed a Russian or Soviet military aircraft since the 1950s, and Russian and Turkish assets fell on fears of an escalation between the former Cold War enemies.

A Kremlin spokesman said it was a "very serious incident" but that it was too early to draw conclusions.

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Footage from private Turkish broadcaster Haberturk TV showed the warplane going down in flames in a woodland area, a long plume of smoke trailing behind it. The plane went down in area known by Turks as "Turkmen Mountain", it said.

Separate footage from Turkey's Anadolu Agency showed two pilots parachuting out of the jet before it crashed. A Syrian rebel group distributed a video that appeared to show one of the pilots immobile and badly wounded on the ground and an official from the group said he was dead.

The Turkish military said the aircraft had been warned 10 times in the space of five minutes about violating Turkish airspace. Officials said a second plane had also approached the border and been warned.

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"The data we have is very clear. There were two planes approaching our border, we warned them as they were getting too close," a senior Turkish said. "We warned them to avoid entering Turkish airspace before they did, and we warned them many times. Our findings show clearly that Turkish airspace was violated multiple times. And they violated it knowingly."

Broadcaster CNN Turk earlier reported that one of the pilots was in the hands of Turkmen forces, who were also looking for the other one, in Syria. Russian military helicopters were also searching for the pilots, Turkey's Dogan news agency said.