Having a Palestinian leader opposed to violence is key to US policy in the region, and Abbas has filled that role for the past six years. A turbulent transition could seriously weaken any new leader.
The issue of succession is so sensitive that it is rarely discussed openly by the Palestinian elite, and Abbas is touchy about it.
When a US newspaper wrote about the leadership ambitions of key players in his Fatah movement, the official Palestinian news agency ran a scathing statement directed at one of those mentioned in the article, former Palestinian envoy to the UN, Nasser Al-Qidwa.
Abbas also went after another Fatah leader, Mohammed Dahlan, stripping him of privileges and shutting down his TV station earlier this month, after Dahlan criticized the president in meetings with activists.
Abbas aides play down concerns about his health, prompted by his smoking and recent weight gain. They say he's fine and that getting dental implants was his only recent medical procedure. Occasional threats to step down are simply attempts to create leverage vis-a-vis Israel and the US, they say.
At the root of the succession problem is the split of the Palestinian territories between Fatah, which now controls the West Bank, and the Hamas movement, which wrested control of the Gaza Strip from Abbas in 2007.
Fatah and Hamas have been unable to reconcile, and their rivalry has prevented presidential and legislative elections, which should have taken place by this year.
Abbas was elected to a four-year term in 2005. The Hamas-dominated Parliament stopped functioning long ago, in part because Israel arrested many Hamas legislators.
Palestinian law calls for the speaker to serve in a 60-day caretaker capacity until elections to replace a president.
This arrangement was used in the transition from Yasser Arafat, who died in November 2004, to Abbas two months later. However, the current Parliament speaker is from Hamas, and it's unlikely Fatah would agree to let Hamas take over the presidency, even temporarily.
Elections also are seen as improbable since they are tied to elusive reconciliation. In this case, Fatah would have to appoint a successor, though the nominee would be vulnerable to claims by Hamas and others that he has no legitimacy.
Fatah, which has long dominated Palestinian affairs, has been in disarray since it lost Parliament elections to Hamas in 2006, with voters punishing the former ruling party for arrogance and mismanagement. Fatah's troubles have been compounded by its failure to establish an independent Palestinian state. If elections were held, it's not certain Fatah would defeat Hamas.
The most popular Fatah leader of the middle generation is Marwan Barghouti, who is in his late 40s, but he is serving five life sentences in Israel for his role in the armed Palestinian uprising earlier this decade.
Among the remaining contenders, rivalry is so intense they might be unable to agree on a consensus candidate or settle on a weak one.
“Fatah suffers a leadership crisis,” said Palestinian analyst Khalil Shekaki. “So far it hasn't presented a No. 2 leader.” Abbas wanted a vice president and early in his term called for creating such a position, said an aide, Nabil Shaath.
However, once the Parliament stopped functioning, it was no longer possible to make the necessary changes in the law, Shaath said.
Abbas hasn't openly designated a favorite in Fatah, though he has given a push to chief negotiator Saeb Erekat, perhaps his most loyal aide. Abbas lobbied for Erekat in Fatah elections in 2009 and gave him a coveted seat in the PLO Executive Committee, a key decision-making body.
Another name being floated by political insiders is Al-Qidwa, whose international experience at the UN and family ties to Arafat — he is the iconic leader's nephew — are seen as a plus.
Al-Qidwa was the one named in the Abbas-authorized response to the newspaper report on the succession battle.
The commentary, published by the official news agency Wafa, complained that local politicians were engaged in rumor-mongering. Al-Qidwa denied involvement and has since patched things up with the Palestinian leader.
Former security chiefs Dahlan and Jibril Rajoub also are perennial contenders. Rajoub, who withdrew from politics for a few years, is building a new base as a successful head of the Olympic and football federations.
Dahlan, the former security chief in Gaza, has lost much of his standing. He was widely held responsible by party colleagues for the loss of Gaza to Hamas and has been dogged by corruption allegations. His problems with Abbas started last month, after he criticized the Palestinian leader in meetings with activists. Both Dahlan and Al-Qidwa declined comment.
The Palestinian politician seen by many Western diplomats as most suited for the job is Salam Fayyad, who as prime minister is overseeing a widely praised state-building program.
However, the political independent has a strained relationship with Fatah leaders and lacks his own power base.
For now, Abbas is determined to stay on, despite his growing frustration over lack of progress in peace efforts, said Azzam Al-Ahmed, a senior Fatah official.
In the most recent setback, the US dropped attempts to persuade Israel to extend a construction slowdown in Jewish settlements, meaning the road to renewed negotiations is effectively closed.
“President Abbas is disappointed, but not to the degree of leaving the stage,” Al-Ahmed said.
