A Turkish official said that two warplanes approached its border with Syria and were warned before one of them was shot down.
Turkey had information showing its airspace had been repeatedly violated, the official said.
Moscow said it could prove the jet had not left Syrian air space.
Turkey has shown it is willing to take on Russia after downing a Russian fighter jet.
This incident will leave the American military profoundly alarmed that the Syrian conflict is now threatening to spiral out of all control.