The statement of the Quartet - the United Nations, Russia, the European Union and the United States - voiced deep concern over the latest surge of violence in the Gaza Strip, which left more than 20 Palestinians dead and over 200 wounded since shooting began between gunmen of Hamas opposition Fatah.
The Russian minister said the statement "confirms all the fundamental principles on which we are striving to achieve a long-term, stable, comprehensive settlement to the Middle East conflict."
"Russia's position is fully reflected in the document which was approved today," he said.
The foreign minister said Russia will pressure the ruling Palestinian Islamist group Hamas to implement proposals put forward by the Quartet.
"Not all members of the Quartet have relations with Hamas, but what we are doing is aimed at implementing the position of the Quartet," Lavrov said.
The minister also said Syria should be brought into the Palestinian-Israeli peace process.
"We support bringing into the peace process all sides who can help make progress, and Syria could play a substantial role in this," he said.
Lavrov also said there must be a viable government in Palestine, ready for talks with Israel.
