Top UN diplomats are pleading for a two-state solution, saying there is a risk of generations of violence unless the leaders act.
However, both sides continue to blame one another for the region's problems.
It has been two weeks since a detailed report aimed at reviving the Middle East peace process between Israel and the Palestinians was released.
The report by the Middle East Quartet -- the European Union, Russia, the United Nations and the United States -- calls on Israel to stop expanding settlements and the Palestinians to stop inciting violence.
It offers 10 recommendations to end the stalemate, resume a transition to greater Palestinian authority in the West Bank and open the way to talks resolving all final-status issues.
The UN Security Council is currently debating whether to endorse the report's findings.
UN secretary-general Ban Ki-moon has urged the council to get behind the Quartet's findings despite strong resistance from Israel and the Palestinians.
"Late last month, I returned from my 11th visit to Israel and Palestine as a secretary-general. As it happened, it was also as Israel's occupation entered its 50th year. I carry a clear and consistent message to leaders on both sides: Time is running out. As negative trends grow more frequent, the prospects of a two-state solution grow more distant. The parties will have to make the necessary compromises for peace."
Ban Ki-moon says he wants a two-state solution to overcome what he terms the "political paralysis," but neither side is satisfied with the Quartet's report.
Arab diplomats agreed during a recent meeting to try to block any move by the Security Council to adopt it.
The Permanent Observer of the State of Palestine to the United Nations, Riyad Mansour, says the report fails to adequately deal with many sensitive issues.
"This includes the report's glaring failure to appropriately deal with the ongoing criminal actions, illegal measures and constant provocations being perpetrated by Israel, the occupying power, against our people and land. It also includes the repeated inappropriate attempts to draw symmetry between the occupying power and the occupied people and to equate individual acts of violence with the official, deliberate policies and actions of the occupying power, which are the source of this conflict and all of its ills."
But Israeli ambassador Danny Danon says his government believes Palestinian Authority president Mahmoud Abbas is ultimately to blame for the individual acts of violence.
He also maintains direct negotiations are the only path to achieving peace.
"There is a direct line between the incitement to hatred spread by Abbas's Palestinian Authority and the despicable acts of terrorism taking place in Israel. The international community must send a clear message to the Palestinian leadership: Stop inciting, and start talking. Israelis want and pray for peace. But we cannot make any progress unless the Palestinians put an end to terror and incitement and finally agree to direct, face-to-face negotiations. Yet, time after time, the Palestinian leadership has failed on both counts."
Since October, Palestinian street attacks have killed at least 33 Israelis and two visiting United States citizens.
Israel has killed at least 202 Palestinians, 137 of them allegedly assailants.
The United Nations' special coordinator for the region, Nickolay Mladenov, says he believes a solution is a more remote possibility than ever.
"It is perhaps the furthest away it's ever been. And, in fact, it may be worse than that -- it is slipping away as we speak. And it's time both for the international community and for the leadership on both sides to wake up. The only alternative that I see is perpetual violence."
France is leading a renewed push to put peace efforts back on the agenda and to bring the two sides back to negotiations by the end of the year.