In a private appearance with Jewish leaders in New York on Monday night, a conciliatory Palestinian Authority President Mahmoud Abbas said he felt the time to reach a peace settlement in the region was running out and signaled his willingness to sit down with Israeli leaders in the near future, several attendees have told The Huffington Post.

Abbas is in the United States for the opening session of the United Nations General Assembly. He is scheduled to address the gathering on Thursday.

In an unscripted moment in New York, first reported by the Israeli daily Haaretz, Abbas also appeared to embrace a plan, initially proposed by the staunchly pro-Israel Harvard law professor Alan Dershowitz, to bring Palestinians and Israelis back to the negotiating table in the near future. The plan calls for Israel to declare a "conditional freeze" on settlement activity that would take effect as soon as the talks began in earnest. Mideast experts suggest that such a plan might help alleviate the reluctance on both sides to make the first move, a concern that has helped paralyze the process ever since a 10-month settlement freeze in 2010 bore no fruit.

The plan, which Dershowitz proposed in a June Wall Street Journal op-ed, came up Monday when Dershowitz found himself in a conversation with Abbas and Saeb Ereikat, the chief Palestinian negotiator.

"I showed the article to him and said, 'This has a chance of breaking the stalemate. Would you be willing to sit down and negotiate on these terms?'" Dershowitz told The Huffington Post.

Dershowitz said that after Abbas passed the article to Ereikat and then read it himself, the Palestinian president encircled the pivotal sentence of the op-ed -- calling for both sides to sit down under a conditional freeze -- and signed and dated it.

An official with the Palestinian diplomatic mission in Washington, D.C., said he would not comment on the details of the event, but indicated that he took issue with some of the accounts of the meeting.

Robert Wexler, the former Florida congressman and current president of the S. Daniel Abraham Center for Middle East Peace, which hosted the event, told HuffPost that the exchange indicated Abbas was "genuinely interested in finding a formula to get back to negotiations."

"Any time American Jewish leaders meet in a constructive way with President Abbas, I think it can have positive reverberations," Wexler added.

Several attendees at the meeting described Abbas as seeming despondent about the turmoil and popular uprisings taking place in the region, and in particular the unrest spreading to the West Bank.

"We are surrounded by the Arab Spring," Abbas said, according to notes of the event provided by a third source who participated in the meeting and requested anonymity to offer greater details about Abbas' remarks. "Because of that, I'm saying take this opportunity now, find peace now, conclude the peace now. Otherwise it will never happen."

According to those notes, Abbas pointed to the uprisings in his own backyard and suggested -- not for the first time this week -- that he's even being urged to consider dropping the Oslo Accords, which dictate that the Palestinian Authority is responsible for security in the Palestinian territories.

"The situation in the West Bank is very critical," Abbas said according to the notes. "We have demonstrations every day, everywhere in the West Bank. We have financial problems ... We have a very bad atmosphere."

He went on, "One of these proposals I heard from our leadership, that it's better that the Oslo agreement is no longer valid ... [that we might] ask Prime Minister Netanyahu to come to Ramallah to take over the authority: As you handed it to us in 1994, come and take back the responsibilities.”

At other moments Monday night, the third participant said, Abbas explained that he had decided not to renew his effort to seek Palestinian statehood at the United Nations this week after being personally asked to hold off by Secretary of State Hillary Clinton, who he said argued that it would only cause undue turmoil with the U.S. election coming up.

Asked to comment on Abbas' remarks about Clinton, a State Department official said only that the administration continues to oppose "a unilateral bid for Palestinian statehood" at the U.N.

Abbas said he would still call for a vote in the General Assembly, according to several sources, but not until the day after the American election.

He also hinted that he would include a line in his U.N. speech on Thursday recognizing the historical Jewish connections to the city of Jerusalem, something he had been criticized for not doing a year before.

"For him to specifically intimate that he will address the question of a Jewish connection to the land of Jerusalem in his speech, that would be a very significant breakthrough," Wexler said. "I'm confident it would be warmly received in Israel as a very important gesture."

CLARIFICATION: An earlier version of this story said that Mahmoud Abbas suggested it might be time to consider dropping the Oslo Accords. Abbas said that Palestinian leaders had suggested to him that it might be time to consider dropping the Oslo Accords.