JERUSALEM, Oct 26 (Reuters) - Israel and the Palestinians have agreed to make proposals on issues of territory and security within three months, keeping peacemaking efforts alive, an official from the Quartet of Middle East peace mediators said on Wednesday.

Representatives from both sides met envoys of the Quartet -- made up of the United States, Russia, European Union and United Nations -- after previous attempts to jumpstart peace negotiations had fallen short.

The parties agreed with the Quartet to come forward with comprehensive proposals on territory and security within three months in the context of our shared commitment to the objective of direct negotiations leading toward an agreement by the end of 2012, a U.N. official said on behalf of the Quartet.

Territory and security are two issues that have held up Israeli-Palestinian peace talks, which collapsed about a year ago in a dispute over Israeli settlement building in the occupied West Bank.

The Quartet envoys also called on the sides to resume direct bilateral negotiations without delay or preconditions and said they would meet the parties regularly over the next 90 days.

Prime Minister Benjamin Netanyahu's office said in a statement after his top negotiator met the Quartet envoys that Israel was interested in restarting direct talks without preconditions.

Palestinian negotiator Saeb Erekat, after meeting the Quartet officials, said in a statement that the Palestinians were prepared to sit at the negotiating table as soon as the Israeli government freezes all settlement construction and accepts clear terms of reference, specifically the 1967 borders.

In the absence of peace talks, Palestinian President Mahmoud Abbas has sought statehood recognition in the United Nations, a move opposed by Israel. (Reporting by Ari Rabinovitch)