"We demand that the Turkish authorities take immediate steps to apprehend Alparslan Celik and his accomplices and bring them to justice for the murder of the Russian pilot," foreign ministry spokeswoman Maria Zakharova said in a statement.
In an interview published Sunday in Turkish newspaper Hurriyet, Celik -- a Turkmen rebel and citizen of Turkey -- said that his "conscience cannot be bothered by a person who threw bombs at Turkmen civilians every day," referring to the slain Russian pilot.
"Revenge is the most natural right," Celik said in the interview, while refraining from claiming the pilot's death.
Moscow and Ankara have been locked in a bitter spat over the downing of the Su-24 jet on November 24, with the Kremlin imposing a raft of economic sanctions against Turkey.
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Zakharova said that the publication of Celik's comments in a major Turkish newspaper had angered and surprised Moscow, and accused the media outlet of being a "platform where terrorists and murderers brag about their crimes and spread hate of Russia and the Russian people through nationalist ideology."
Turkish authorities have accused Russia of "ethnic cleansing" in Syria, targeting Turkmen and Sunni population that oppose the regime of Syrian President Bashar al-Assad, Moscow's long-time ally.
Turkey says the Russian jet strayed into its airspace and ignored repeated warnings, while Moscow insisted it did not cross over from Syria and accused Ankara of a planned provocation.