Tzipi Livni, the Israeli foreign minister, and Mahmoud Abbas, the Palestinian president, will report to the representatives of the Quartet - the United States, the European Union, Russia and the United Nations - on their slow-moving efforts.
Livni has said that she would not sign "any agreement that does not serve Israel's interest and that is not detailed enough to be put into effect".
"We are not there yet and it could take time. But we have managed to ensure that this process remains bilateral and that the world does not intervene in the contents of the talks and that it supports the process without trying to impose solutions or present interim solutions," she said.
Nour Odeh, reporting from Cairo, said that meeting reflects much of the same attempts at peace in the past.
"What is interesting here however is that the Quartet has decided to forbid itself from exercising control to make the parties talk," she said.
"They are letting the sides talk it out on their own, yet their mandate is to somehow enforce dialogue. It reflects the stance of the Quartet, that perhaps peace really is elusive here and another approach may be needed."
Last November in Annapolis, Israeli and Palestinian leaders revived negotiations aimed at resolving core problems such as the status of Jerusalem, the borders of a future Palestinian state and the right of return for Palestinian refugees.
Al Jazeera's Amr El-Kahky, reporting from Sharm El-Sheikh, said that the Palestinians are determined to seal a deal.
"The Palestinians are coming with one goal - to get everything or nothing. They want to go into final status talks, and not point by point assessments, because they say they are tired of talking," he said.
"But bear in mind there is a vacuum in Palestinian politics, as well as the current political turmoil in Israel. Therefore it is very diffcult for any progress to be made."
"The distance to peace has been narrowed although peace has not been achieved," Rice said after meeting Abbas on Friday.
In the absence of a full accord, Rice is pushing the two sides to define the outlines of a deal before she hands over to the administration of Barack Obama, the US president-elect.
"One of the things we must do is that we must show ... that Annapolis has laid the foundation for the establishment of the state of Palestine," she said.
Rice has visited the region at least 19 times in the last two years but there have been few tangible signs of progress.
Sunday's meeting will also be attended by Sergei Lavrov, Russia's foreign minister, his French counterpart Bernard Kouchner, Javier Solana, the EU foreign policy chief, and Ban Ki-moon, the UN secretary general, will also be present.
The situation been further complicated by the ongoing feud between Hamas, which seized full control of the Gaza Strip in 2007, and Abbas's Fatah party, which currently only has power in the West Bank.
Reconciliation talks between the rival groups and other Palestinian factions which were due to take place on Monday in Cairo, the Egyptian capital, have been cancelled after Hamas announced a boycott.