JERUSALEM — Two weeks after the Palestinian president, Mahmoud Abbas, vowed not to run for re-election and hinted that he might resign, the Middle East peace process has sunk into a deep crisis amid urgent efforts to revive it.

The Israeli security establishment is in a state of alarm over the possible departure of Mr. Abbas, whom it considers a genuine moderate. Some of its top members are urging their government to make far-reaching offers — “not just lifting a few roadblocks,” in the words of one — that would persuade him to stay in power and resume negotiations with Israel on a solution that involves creating an independent Palestinian state.

Palestinian leaders are looking elsewhere for salvation. Aware of their own weakness, but also of rising disillusionment abroad with Israel over West Bank settlement growth and its war in Gaza in January, they are hoping to turn frailty to their advantage by appealing to the international community to come to their rescue.

Meanwhile, the Obama administration and European governments are also seeking ways to restart the peace talks and keep Mr. Abbas in place.

“Everyone is running around in circles trying to rebuild this process, to find some way to start it up again,” a senior Israeli official observed. “No one knows if it is possible.”

Mr. Abbas has repeatedly stated that the only way forward is with a complete Israeli freeze on settlement building in the West Bank and East Jerusalem. Israel’s prime minister, Benjamin Netanyahu, has offered to greatly reduce building, but not to stop it — and added that East Jerusalem would not be included. His government just announced plans to build hundreds of new units in a part of the city captured in 1967.

Mr. Abbas’s threat stems from many causes, but essentially from his belief that Israel is unwilling to accept Palestinian demands on settlements, Jerusalem and the return of Palestinian refugees. Officials on all sides agree that the gaps between the two sides on these issues appear unbridgeable for now.

“He is at a point where he can no longer pretend that this role of presidency will lead him to helping the Palestinians overcome occupation,” said Nader Said, a sociologist who runs Arab World for Research and Development, in Ramallah. “It doesn’t seem that there is any seriousness on the Israeli side to establish a Palestinian state and no desire on the part of the Americans to deliver the goods.”

Mr. Abbas has joined his chief negotiator, Saeb Erekat, in seeking approval by the United Nations Security Council of the declaration of a Palestinian state without Israel’s agreement.

“We are now facing a moment of truth,” Mr. Erekat said recently. “We will seek to pass this Security Council resolution and the activation of the Fourth Geneva Convention to protect the Palestinian people.”

Washington and the European Union have called such a move premature while Prime Minister Netanyahu warned that it would be met by unilateral Israeli steps. The only way forward, he said, was through renewed talks.

American and Israeli officials are contemplating a series of steps to persuade Mr. Abbas to stay. They include a marked intensification of security and economic cooperation, more money, invitations to Western capitals, robust statements of support, prisoner releases and efforts to draw Arab states more fully into the process.

Over the past year and a half, Palestinian security forces have moved into West Bank cities and taken over responsibilities previously filled by the Israeli military. But about 60 percent of the West Bank remains fully in Israeli hands, and some suggest yielding part of that area to the Palestinians right away and increasing Palestinian responsibilities in the other areas.

Salam Fayyad, the Palestinian prime minister, opposes seeking international recognition of a state. Instead, he has put forth a two-year plan aimed at building institutions and security so that the future state will be strong, transparent and well run.

It is far from clear if he can carry it out. The Palestinian Authority is hundreds of millions of dollars short of making its monthly payroll, and major Arab donors, like Saudi Arabia, have refused to make contributions. Moreover, Mr. Fayyad, a political independent, may not have the support in the bureaucracy to make the changes he seeks.

The legal status of the Palestinian political system has been in flux since Hamas, the Islamist party, threw the Fatah-dominated Palestinian Authority out of Gaza in 2007. Hamas had won a legislative election the previous year, but a power-sharing agreement between Hamas and Fatah failed. There are now parallel ministries and security services in the two territories. The official term of Mr. Abbas’s presidency has already ended, and the term of the legislative council is scheduled to end in January.

Mr. Abbas called elections for January, but they will be delayed because of the split with Gaza. Egypt has been trying to get Fatah and Hamas to agree to a plan of reconciliation, but so far that has not happened. Hamas has said that without the agreement, there will be no election in Gaza.

Many believe that even if the two sides sign the document, no real reconciliation will follow because the anger between them runs so deep.

“Abbas lost his legitimacy 10 months ago,” Mahmoud Zahar, a top Hamas leader, said in an interview in Gaza this week. “Anyway, he is a tool and property of America.”

Many Palestinians suspect that Mr. Abbas, 74, a longtime associate of Yasir Arafat, Fatah’s founder, will simply stay in his post during the election delay. “I don’t see him leaving for the next year,” said Mahdi Abdul Hadi, who leads the Palestinian Academic Society for the Study of International Affairs in Jerusalem.

The Palestine Liberation Organization, the supreme authority of the Palestinian people, will most likely meet in the coming weeks, declare Mr. Abbas’s term extended and paper over other legal conundrums.

Mr. Abbas has not groomed a successor. The American and Israeli dream would be Mr. Fayyad, but besides having no political base, he is not a member of Fatah, so Palestinians consider the prospect highly unlikely. More possible, a few say, would be for Mr. Abbas to remain president while allowing Mr. Fayyad to carry out his reform plan.

Two former security chiefs, Muhammad Dahlan and Jibril Rajoub, are also possibilities, although there seems to be no groundswell around them and plenty of opposition. Muhammad Ghneim, a founder of both Fatah and the P.L.O. who came to the West Bank this past summer from exile, is considered a possible place holder if the job suddenly becomes vacant. And Nasser al-Kidwa, a nephew of Mr. Arafat and former Palestinian envoy to the United Nations, is also mentioned by some as a possible future candidate.

But there is no appetite for a succession struggle as everyone waits to see whether the peace process deadlock can be broken.