The recordings, made available to The Associated Press today, indicate that the plane was warned several times that it was approaching Turkey's airspace and asked to change course.
Turkey shot down the Russian Su-24 bomber on Tuesday, insisting that it had violated its airspace despite repeated warnings.
A surviving Russian pilot has denied that his jet veered into Turkey's airspace and rejected Turkey's claim that it had issued repeated warnings to the Russian crew.
In the recordings, a voice is heard saying in broken English: This is Turkish Air Force speaking on guard. You are approaching Turkish airspace. Change your heading south immediately. Most of the audio is garbled and barely comprehensible but the tone of the voice gets more agitated as the warnings appear to go unnoticed.
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Tuesday's incident was the first time in half a century that a NATO member shot down a Russian plane. Russia said yesterday it will deploy long-range air defense missiles to its base in Syria and destroy any target that may threaten its warplanes.
A Russian marine was also killed by the militants during the rescue mission.
Speaking in televised comments from the Russian base in Syria, the surviving navigator of the downed plane, Capt Konstantin Murakhtin, maintained the plane did not enter the Turkish airspace "even for a single second.