The warning reflects desperation, but may not signal action.
Abbas' hopes of setting up a Palestinian state through negotiations with Israel have been derailed, and a new poll shows that a majority of Palestinians want the 80-year-old to resign and dissolve his self-rule government, the Palestinian Authority. Many no longer believe a two-state solution is realistic and support political violence.
Abbas could try to align himself with a frustrated public by shifting to a more confrontational policy, including ending security cooperation with Israeli troops against a shared foe, the Islamic militant Hamas group.
It's a risky move that could cost him vital foreign aid, trigger chaos and end his 10-year rule. Abbas aides have suggested in recent days that despite his threats, he will make do with a general warning to Israel at the U.N.
Yet more indecision could further turn Palestinians against him. The mood in the West Bank is explosive, with anger mounting over Palestinian Authority mismanagement, perceived Israeli threats to a major holy site in Jerusalem and a sense of having been abandoned by the Arab world, said veteran pollster Khalil Shikaki.
"If a spark comes along, there is absolutely no doubt that the Palestinian situation today is very, very fertile for a major eruption," he said.
Here is a look at what lies ahead.
On the sidelines
Just three years ago, Abbas was the center of attention at the annual U.N. gathering of world leaders. He asked for, and later received, General Assembly recognition of Palestine as a non-member observer state in the West Bank, Gaza and east Jerusalem, the lands Israel captured in 1967.
But when Abbas addresses the General Assembly on Wednesday other regional conflicts, including the war against the Islamic State group and the migration crisis in Europe, are likely to take the spotlight.
President Barack Obama made no mention of the Israeli-Palestinian conflict in his speech to the General Assembly on Monday, drawing rare public Palestinian criticism.
"Does Obama believe that he can defeat Islamic State and terrorism or achieve security and stability in the Middle East by ignoring the continued Israeli occupation...?" Abbas aide Saeb Erekat said in a statement published by the official Palestinian news agency WAFA.
Washington appears to have little interest in mounting another major push for peace. A nine-month effort by Secretary of State John Kerry collapsed last year because Abbas and Israeli Prime Minister Benjamin Netanyahu couldn't even agree on the ground rules. Netanyahu, unlike some predecessors, refuses to recognize Israel's pre-1967 frontier as a starting point for border talks.
What can Abbas do?
Statehood through negotiations has been his sole strategy for decades and he opposes violence. With those options off the table, Abbas tried to gain leverage by courting further international recognition, including by joining institutions such as the International Criminal Court.
But any possible ICC war crimes case against Israel for settling on occupied lands is years away, if it's possible at all. And symbolic victories, such as the right to raise the Palestinian flag outside U.N. headquarters this year, mean little to Palestinians struggling with unemployment, and rising prices.
In recent weeks, Abbas resorted to threats to remind the world that the Israeli-Palestinian conflict must not fester. He warned he is fast-tracking his retirement, hinted at dramatic changes in dealings with Israel and said he would "throw a bombshell" at the end of his U.N. speech. But he has not elaborated.
Whats in the speech?
Abbas will make his decision only after talks with Kerry and other Arab and European mediators in New York, aides said.
In a weekend meeting, Kerry did not offer Abbas sufficient guarantees if he gives peace efforts another chance, Abbas adviser Ahmed Majdalani told Voice of Palestine radio.
Palestinian U.N. ambassador Riyad Mansour told the station that Abbas' speech is to "present steps to create facts on the ground toward setting up statehood, the statehood how we see it, how the international community sees it, not how the occupation (Israel) sees it."
Abbas will likely complain about Israeli actions, including settlement expansion and army incursions into autonomous Palestinian areas, said Majdalani and another aide, Nabil Shaath.
They suggested the Palestinian leader will not go beyond general warnings, but Shaath cautioned that last-minute changes are possible.
Some senior Palestinians raised the idea that Abbas request U.N. trusteeship, but the option was dropped on legal grounds, officials said.
How durable is the status quo?
The Oslo Accords that set up Palestinian autonomy in the mid-1990s were meant as a stepping stone toward Palestinian statehood. Instead, a temporary arrangement has largely remained in place despite wars, uprisings and political crises. Hamas seized Gaza in 2007, but Abbas still administers 38 percent of the West Bank, with the rest of that territory and Israeli-annexed east Jerusalem under sole Israeli control.
The arrangement serves both sides to some extent. Israel has given itself free rein on security, while successfully subcontracting some security tasks to Abbas' forces. The Palestinian Authority, supported by millions of dollars in foreign aid, provides public services, relieving Israel of its costly burden as military occupier.
The Palestinian Authority has become the largest employer in the West Bank, while the political class enjoys many perks, such as preferential access to housing and jobs.
"Abbas is not going to dissolve the Palestinian Authority because there is an internal interest in maintaining it, the privileges, the international pressure and the international money," said Ali Jerbawi, a former Palestinian Cabinet minister.
What does Israel want?
Netanyahu has accused Abbas of fomenting violence through alleged incitement, as tensions have risen around Jerusalem's most sensitive holy site, revered by Muslims and Jews. But despite the rhetoric, Netanyahu appears to have little interest in seeing Abbas go.
Netanyahu faces growing international isolation due to anger over settlement construction and stalled peace efforts. The collapse of the Oslo accords would raise pressure on Netanyahu to try to resolve the Palestinian issue. Netanyahu has called for a resumption of peace talks, but has not said what he might offer.
Abbas has lost Palestinian public opinion, according to last week's poll by the Palestinian Center for Policy and Survey Research, based on 1,270 respondents, with an error margin of 3 percentage points.
"Two-thirds of the public want him out, they demand that he resign," said pollster Shikaki.
But there is no clear path to change.
If presidential elections were held today, Abbas would lose to Ismail Haniyeh, the top Hamas leader in Gaza. However, elections are unlikely because of the political and geographic split between the West Bank and Gaza. No obvious successor to Abbas has emerged from within his inner circle.
Palestinian anger is rising-- in some ways reminiscent of the mood before the outbreak of the second uprising 15 years ago, Shikaki said. At the same time, Palestinians are still scarred from the harsh Israeli clampdown following the bombings and shootings of the last revolt, and there might be little appetite for renewed hardship.
Mohammed Ennayah, a pharmacist in the West Bank, said Abbas failed and should resign.