The resolution stated that U.S.-brokered talks between Israel and the Palestinians were "irreversible." It also called on both sides to step up efforts to reach a lasting peace.
The resolution was designed to encourage the peace process. However, it does nothing to resolve the region's most acute problems - in particular, defining Jerusalem's status, resolving the issue of the return of Palestinian refugees, and the future borders of a Palestinian state.
The resolution also supported Russia's offer to host an international meeting on the Middle East in Moscow in 2009.
The Quartet of negotiators on the Middle East conflict - the United States, Russia, the European Union and the United Nations - held a ministerial meeting at the UN headquarters in New York late on Monday and issued a statement on the situation in the Middle East.
"The Quartet expressed its considered view that the bilateral negotiations process launched at Annapolis is irreversible and that these negotiations should be intensified in order to put an end to the conflict and to establish, as soon as possible, the State of Palestine, living side by side in peace and security with Israel," the statement said.
Talks between Israel and the Palestinian Authority, launched by U.S. President George Bush in November last year at a conference in Annapolis, Maryland, have been stalled by an outbreak of violence in the Middle East, as well as long-standing disputes over the construction of Jewish settlements and the future status of Jerusalem.
Russian Foreign Minister Sergei Lavrov said on Tuesday that the holding of an international Mideast conference in Moscow could speed up the peace process, in particular with regard to agreements reached between Israel and Palestine.
"Only together and on a commonly recognized international-legal foundation can we achieve a just, firm, and comprehensive peace settlement," he said at the UN Security Council meeting.