He said a Russian official would soon travel to the province of Hatay together with a Turkish military official and receive the body.
Mr Davutoglu added that Lt Col Peshkov's body had been treated in accordance with Orthodox Christian tradition.
Another pilot in the plane, Capt Konstantin Murakhtin, survived and was rescued from rebel-held territory in Syria in a special forces operation.
Capt Murakhtin said he wanted to go back to duty and stay in Syria, saying "someone has to pay" for his colleague's death.