The fate of the two pilots who ejected from the downed plane is unclear. Turkey had objected last week that Russia was bombing Turkmen rebels in Syria.
Kurds are considered the largest ethnic group in the world without a country. The turmoil in Syria and Iraq creates an opportunity to draw closer to that dream.
Russia's military intervention in Syria has jolted NATO and provoked frustration in Washington. On Wednesday, Russia launched cruise missiles from warships in the Caspian Sea.
Russian jets have twice entered Turkish airspace, according to NATO, which has disputed Russia's account of an accidental incursion during action in Syria.
Turkey has vowed to step up its campaign against the outlawed PKK. The collapse of its cease-fire with the PKK has complicated the US-backed campaign against the self-proclaimed Islamic State.
The outlawed PKK separately attacked a Turkish military brigade in southeast Turkey. Analysts say Turkey is prioritizing air strikes against Kurdish militants over strikes against the self-styled Islamic State.