ISTANBUL — Turkey took steps on Friday to calm relations with Russia over the shooting down of a Russian warplane this week, calling for a presidential-level meeting, possibly at the climate talks in Paris next week.

“I would like to meet Putin face to face in Paris,” President Recep Tayyip Erdogan said in a speech on Friday, referring to President Vladimir V. Putin of Russia. “I would like to bring the issue to a reasonable point. We are disturbed that the issue has been escalated.”

As that invitation was issued, the Turkish prime minister, Ahmet Davutoglu, said that Ankara would “work with Russia and our allies to calm tensions.”