"It's Russian-made, but Russia has told us it doesn't belong to them," PM Ahmet Davutoglu said during a television interview.
Turkey shot the drone down on Friday after it violated its air space near the Syrian border despite three warnings.
Davutoglu said it could have belonged to Syrian government forces -- to whom Russia supplies arms -- or Kurdish armed groups in Syria, or "it could belong to a militia".
The US military had said it believed the drone was of Russian origin, but Moscow said all its drones were accounted for.
The country has accused Russian aircraft operating in Syria of violating its air space twice, with Moscow blaming poor weather.
Davutoglu today warned Moscow against repeating the incursion, saying the drone "incident has once again proved that Turkey both has the capacity and the political will to put an end to such violations."
"I hope that Russia will adopt a more careful stance... and Turkish-Russian relations will not be negatively affected," he said.
