Alexander Kalugin, the Russian Foreign Ministry's special envoy, said the current situation in the region would be discussed at the meeting.
He said a meeting of the ministers of the quartet would be held during September's session of the UN General Assembly in New York.
"The parties will review the initial results of the [settlement] process and outline further steps there," the Russian diplomat said.
He said Russia praised Israel's withdrawal from the Gaza Strip and the northern sector of the West Bank and saw it as just the beginning of movement toward a stable peace between the Israelis and the Palestinians.
"Our guideline is the road map, in which the parties' commitments are precisely fixed," Kalugin said. "In particular, the Palestinians must complete disarmament to provide for a single authority and uniform law, and prevent terrorist attacks; the Israeli party must stop settling activity, withdraw troops from the occupied territories, and strive to make the situation similar to that of September 2000."
He said Moscow did not expect the peaceful settlement process to be completed in the near future.
"There are a great deal of difficult questions, which is why we are realistic about the situation, and we do not expect any breakthroughs soon," the official said.
