Davutoglu, 56, said that Russia's comments reminded him of his youth when NATO member Turkey and the Soviet Union were on opposing sides in the Cold War.
"There was a Soviet propaganda machine in the Cold War era," Davutoglu told reporters at an Ankara airport before leaving for Azerbaijan on an official visit.
"They were called Pravda lies," he said, referring to the daily newspaper that was the mouthpiece of the Communist Party.
"Russia's Sovietic stance - that we thought it had forgotten - is coming back bit-by-bit," he said.
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Russia "operates a propaganda machine in order to cover up" problems it encounters with its neighbours.
"Nobody gives credit to this Soviet propaganda machine's lies."
The shooting down by Turkish F-16 fighter jets of a Russian warplane on the Syrian border on November 24 has sparked the worst crisis in relations between Moscow and Ankara since the Cold War.
And the tensions have escalated, with Moscow imposing a raft of economic sanctions in retaliation.
The Russian defence ministry yesterday claimed Turkish President Recep Tayyip Erdogan and his family were involved in the illegal oil trade with IS.
Erdogan rejected the claims as Russian "slander" and said he was ready to resign if the claim was proven.