During his visit Abbas will discuss plans for a Middle East peace conference due to be held in Moscow, the Palestinian embassy earlier said.
As well as the conference slated for mid-June, Abbas will discuss relations with Russia, and the Middle East peace process as a whole during talks with Russian leaders, the official said.
Russia is involved in the Mideast peace process as a party to the quartet of mediators along with the United States, the UN and the European Union.
Moscow's plans to host the conference, a follow up to last November's talks in Annapolis, in the U.S., have received the backing of several Mideast states including Syria.
Syria's deputy foreign minister told reporters in Damascus on Monday: "We cannot ignore any international meeting that will discuss our problems, and from all indications the upcoming meetings, especially the Moscow conference, will open the way to a real settlement along all lines of the Middle East peace process," Faisal al Mekdad said.
Since November Russia has urged Mideast states to implement agreements reached in Annapolis and to try to prevent unilateral measures.
The Middle East Quartet is set to gather on April 17 in Amman, the capital of Jordan.
