Ankara is warily watching if Moscow will tighten links with Kurdish factions amid the crisis in bilateral ties following the downing of a Russian bomber by Turkey at the Syrian border last month.
"We know that there are Iraqi and Syrian Kurds who are fighting the threat of Isis and other extremist groups with weapons on the ground," Lavrov told Demirtas, the leader of Turkey's Democratic People's Party (HDP).
"Russia... Is ready to actively cooperate with those on the ground who are fighting this threat," he said in remarks released by the foreign ministry.
Demirtas is the first high-profile Turkish figure to visit Moscow since Turkey shot down a Russian warplane on the Turkish-Syrian border on November 24.
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The incident sparked the biggest crisis in ties between Moscow and Ankara since the end of the Cold War and saw Moscow introduce a raft of economic sanctions against Turkey.
The Turkish government has criticised the visit of the main Kurdish opposition party leader to Russia.
"Why are they going at such a time to a country with which we are having a crisis because of their violation of this nation's airspace?" Turkish Prime Minister Ahmet Davutoglu asked yesterday.
Russia's top diplomat told Demirtas that Moscow's sanctions against Turkey and its position over the warplane downing in no way extend "to our relationship with the Turkish people."
"It is important to unite all the resources of those who seek to decisively battle terrorism," Lavrov added.