The trip by Selahattin Demirtas -- a key rival of President Recep Tayyip Erdogan -- will be the first by a high profile Turkish figure to Russia since the shooting-down of the Russian Su-24 warplane led to a crisis in the two countries' ties unprecedented since the Cold War, Reuters reported.
"The spike in tensions with Russia will inflict a heavy price on Turkey," Nazmi Gur, an HDP lawmaker who will accompany the party leader during the trip to Moscow said.
"Turkey's engulfing itself in problems with its major neighbor will deepen problems including the Syrian crisis. What the peoples of Turkey need is not crisis," he said.
"I hope this initiative (by Demirtas) will help soften relations between Turkey and Russia," he added.
Demirtas had first announced the plan for the trip in an interview with a regional television over the weekend.
After the November 24 shooting down of the plane, Moscow has imposed a raft of economic sanctions on Ankara. Turkey says the Russian jet has violated several times its airspace but Moscow insists it never strayed from the Syrian territory.