Labor's former parliamentary whip, Daniel Ben Simon, suggested Sunday that he would support a breakaway group if efforts to restart peace talks remain deadlocked for the next few months. Israeli media outlets have reported that two Labor ministers may join the rebels.

"We have to make a serious decision about how long we want to stay in the government and under what circumstances," said Colette Avital, a former Labor Party parliament member and former consul general in New York.

The threat to Labor comes as the Palestinian Authority appears in increasing disarray, with President Mahmoud Abbas vowing not to seek re-election next year.

A Labor split could undermine the stability of Prime Minister Benjamin Netanyahu's government and shift its policies further to the right, deepening the impasse with the Palestinians and dashing U.S. hopes to resolve the Palestinian-Israeli conflict.

A splinter party "would shock the coalition of Benjamin Netanyahu in one way or another," wrote Shalom Yerushalmi, a political commentator for the Maariv newspaper. The Labor Party leader, Defense Minister Ehud Barak, "doesn't have a party," Mr. Yerushalmi wrote.

Labor has been a counterweight in Mr. Netanyahu's center-right government. The defense minister is credited with helping to persuade Mr. Netanyahu to support a Palestinian state and smoothing rocky ties with the Obama administration.

But the decision to join a government led by Mr. Netanyahu stirred bitter opposition within Labor. If negotiations with the Palestinians remain frozen, rebels are likely to persuade other Labor members to bolt the governing coalition.

"Barak believes he is doing a good job at moderating the position of the government," Ms. Avital told The Washington Times. "But, I don't think that this is the way that we are going to win elections."

Mr. Barak has enjoyed an unexpectedly strong collaboration with Mr. Netanyahu, who was unseated as prime minister by Mr. Barak in elections 10 years ago. As defense minister, Mr. Barak is a prominent figure in the government, but his popularity is weak.

Under Mr. Barak's leadership, Labor lost six seats in parliament in the last election and currently has 13 seats, a historic low for a party that ruled Israel from its founding in 1948 until 1977, and twice subsequently. It also led Israel through four wars against Arab neighbors.

Splits in major Israeli parties are not new. Kadima, currently the largest party in parliament, was founded in 2005 as a breakaway from Mr. Netanyahu's Likud. But many say that a new fissure in Labor could mark the historic party's final demise.

Ms. Avital noted that Labor has been in turmoil since Mr. Barak lost the prime minister job to Ariel Sharon in 2001. Labor has gone through five leaders and run up a debt of $40 million.

If Mr. Barak is willing to give up the defense ministry and pull Labor out of the governing coalition, Mr. Netanyahu could remain in power. But far-right and religious parties would be in a better position to threaten to topple the government if Mr. Netanyahu is seen as opposing their views.

"Before, no one party could threaten to bring down the coalition. Netanyahu had a wider coalition," said Gideon Doron, a professor of political science at Tel Aviv University. But if Labor pulls out, "he will have a smaller cushion."

That would leave Mr. Netanyahu much less room to offer the "great concessions" that he promised, without elaborating, in a speech Monday at the annual convention of the Jewish Federations of North America. The prime minister added that he doesn't want open-ended talks.

At the moment, there's no near-term prospect of any talks because of a dispute over the continued expansion of Israeli settlements in the West Bank.

Frustrated by the impasse, Mr. Abbas made his threat last week not to seek re-election. He has threatened before to step down; still, aides are trying to counter skeptics who say the latest announcement was a tactical move to pressure the United States and Israel on settlements.

In remarks to the New York Times, chief Palestinian negotiator Saeb Erekat warned that an Abbas departure could leave a vacuum that could bring down the entire Palestinian Authority.

Ghassan Khatib, another government spokesman, said the Palestinian Authority would not fall if Mr. Abbas resigned but acknowledged that the Palestinian government, which lost Gaza to Hamas in 2007, has been weakened by the lack of progress in peace talks.

"The factors leading to the collapse of the authority are the reason for the resignation of Abbas rather [than] vice versa," he said. "I don't see it collapsing."