A ministerial session of quartet members -- the United States, Russia, the European Union and the United Nations - was held in New York late Friday as part of the current session of the UN General Assembly
The Quartet statement said the idea of holding the Moscow meeting in spring 2009 "is acceptable."
Russia as a member of the Quartet of Middle East mediators has offered to host a Middle East peace conference in Moscow as a follow-up to last November's U.S.-sponsored meeting in Annapolis, Maryland.
Israel and the Palestinian National Authority pledged in Annapolis to resume peace talks, draft a settlement plan by late 2008 and come to terms on the form of a future independent Palestinian state. However their talks have so far made little tangible progress.
The Quartet expressed "deep concern about increasing (Israeli) settlement activity, which has a damaging impact on the negotiating environment and is an impediment to economic recovery and called on Israel to freeze all settlement activity."
The construction of settlements, viewed as a major obstacle to reaching a peace deal between Israelis and Palestinians, has nearly doubled since 2007, despite Israel's pledge to freeze such activities.
The Friday meeting ended with a call on Israel and Palestinians to seal peace deal by the end of 2008.