The Russian helicopter had reportedly been scrambled to the crash scene to search for survivors after the jet was shot down following 10 warnings in five minutes to leave Turkish airspace, a Turkish military official has said.
It comes as rebel forces said that bodies of both pilots have been recovered, Al Jazeera reported.
The Russian jet was just over the Syrian border when it was downed by F16 Fighting Falcon jets belonging to Turkey, the Turkish official said.
But the Russian Defence Ministry said the plane had not violated Turkey's airspace and was flying at an altitude of 6,000 metres.
Russian President Vladimir Putin has called an emergency meeting over the downing of the jet and unverified sources have claimed Russia is currently sending a warship across the Dardenelles from the Black Sea into the Mediterranean.
NATO has announced it will be holding an extraordinary session at 4.30pm GMT after Turkey requested it following the incident.
Two pilots managed to eject from the jet and were seen landing with the help of parachutes.
The jet is reported to be a Russian Su-24 flown by a pair of Russian pilots, with one believed to have been captured by Syrian rebels from the Alweya Al-Ashar (Brigade of the 10th) which consists of Turkmen with strong links to Turkey.
The second pilot is believed to have died in the crash after footage was released by Syrian rebels appearing to show them crowding around a body saying "Allahu Akbar" - God is Great in Arabic.
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