Israeli and Palestinian negotiators have until Wednesday before they have to provide U-S President Bill Clinton with their final decisions on the latest U-S proposal for peace between the two sides.
Israeli Prime Minister Ehud Barak said on Sunday that now was the time to make a major push for a Middle East peace deal.
But Palestinians have been more cautious about the proposal, saying key differences remained.
Talks that have taken place between the two sides in Washington over the last week have resulted in a new proposal by the U-S for reaching a settlement.
This focuses on the four major issues of disagreement - Jerusalem, Palestinian refugees, borders and the ending of the conflict in the region.
According to the U-S proposal a Palestinian State would be established on 95 percent of the West Bank and all of the Gaza Strip.
Israel would be sovereign over the remaining five percent of the West Bank which includes Jewish settlement blocs.
Israel, which currently claims sovereignty over all of Jerusalem, would concede control of the Arab neighbourhoods in east Jerusalem to the Palestinians, including most of the walled Old City.
Palestinians would also have control over the disputed Al Aqsa mosque compound in the Old City, an extremely sensitive site sacred to both Muslims and Jews.
Israeli politicians from the right-wing opposition, and even some from within Barak's government, have condemned any concession on the Al Aqsa compound, known to Jews as the Temple Mount.
A special body would be established to deal with Palestinian refugees who fled or were driven out in past wars.
Most refugees would be settled in the countries where they currently reside Jordan, Syria and Lebanon and some would be absorbed into Palestinian areas.
Only a limited number would be permitted to resettle inside Israel.
Palestinian negotiator Yasser Abed Rabbo, who attended the talks in Washington said that until now there has not been enough flexibility in the Israeli position to encourage the Palestinians to say they're close to reaching an agreement.
Rabbo said that the Palestinians were still considering the U-S proposal.
Yasser Arafat went to discuss the plan with Egyptian president Hossni Mubarak, and Israeli Foreign minister Shlomo Ben-Ami briefed Barak on the U-S talks on Sunday.
If they see the potential for progress, Barak and Palestinian leader Yasser Arafat are likely to travel to Washington for talks with Clinton.
According to Ben-Ami, Clinton would then decide whether it was worth convening a Mideast summit.
Time is running short for a deal under Clinton's watch.
He leaves office in four weeks, while Barak faces an uphill battle for re-election as prime minister on February 6.
If a peace deal is negotiated, Barak has said he will consider the election a referendum on the agreement.
But both sides have faced criticism at home over their reported concessions.
Meanwhile, the three months of Middle East violence scared away Christian pilgrims and put a damper on Christmas festivities in Bethlehem, the town of Jesus' birth.
"Once you give them something they want more, so eventually they'll just take us all, they'll control us all - and that's what they want, they don't want peace."
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"I think the proposal is good."
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"We won't accept any proposal that doesn't give us complete guarantees over the implementation of the agreement. For example the presence of international forces to overlook the accurate implementation of an agreement."