Abbas said he "appreciated" Russia's role in the peace process. Both he and Lavrov said they were looking forward to a Middle East conference that Moscow plans to host next year.
Saeb Erekat, a Palestinian negotiator, also speaking before the talks, said that Abbas would be seeking to enlist Russia's support in opposing illegal Israeli settlement building in the West Bank.
"During the discussions he will insist on the necessity that Israel stop building settlements and prevent a rollback to the starting point of the negotiations," Erekat said.
Over the weekend, Abbas visited Grozny, the capital of Russia's war-ravaged region of Chechnya, and met Ramzan Kadyrov, the Chechen leader, in a trip that the Russian newspaper Kommersant said would "undoubtedly" please the Kremlin.
"Mahmud Abbas became the first leader of the Muslim world to fly to Chechnya," the newspaper said, adding that Muammar Gaddafi, the Libyan leader, and Jordan's King Abdullah II had not toured Chechnya on visits to Russia.
"This will undoubtedly please Moscow," Kommersant reported.
Russia is a member of the diplomatic quartet for Middle East peace that also includes the European Union, United Nations and United States.