Yildirim, during an address to a conference at the Moscow State Institute of International Relations (MGIMO) University, described November 2015’s downing of a Russian warplane as an “unfortunate event”.
Relations between Russia and Turkey soured last year after the warplane was brought down on the Syrian border.
Yildirim said relations with Moscow had faced a "test" but added: "Thanks to mutual political will, we have endured the difficult situation."
He recalled the "normalization process" which started from Aug. 9 following a meeting between President Recep Tayyip Erdogan and his Russian counterpart Vladimir Putin in St. Petersburg.
"Due to the nature of the region, we [as Russia, as Turkey] have a crucial duty. At the same time we have responsibility [in the region]," Yildirim added.
Yildirim will meet Chairwoman of the Council of the Federation Valentina Matviyenko and will later hold a news conference with Russian counterpart Dmitry Medvedev.
Bilateral relations, particularly in the economic field, as well as regional and international developments will be discussed during Yildirim's visit.