“Bibi, especially now, cannot and will not concede anything to the Palestinians without getting something he can point to from the Arabs,” said Dennis B. Ross, a longtime Middle East negotiator, using Mr. Netanyahu’s nickname. “Abu Mazen, similarly, won’t do anything toward the Israelis unless there is an Arab cover that offers him an explanation for any move.”

Before the meeting, Palestinian officials complained about the lack of an American plan and the refusal of the administration to reaffirm it support for a two-state solution to the conflict. There were reports that Mr. Abbas would present his visitors with an ultimatum to produce something within 45 days or face the Palestinians defecting from the process.

The Palestine Liberation Organization’s envoy in Washington, Husam Zomlot, was quoted as having told reporters last week that uncertainty could lead the Palestinian leadership to resume its campaign for recognition at the United Nations. Others have proposed more aggressively suing Israel in the International Criminal Court.

On Thursday, however, Mr. Abbas said, “We know that this delegation is working for peace, and we are working with it to achieve what President Trump has called a peace deal. We know that things are difficult and complicated, but there is nothing impossible with good efforts.”

Several experts said the Palestinian threats at this stage were more about trying to exert pressure on the American team than derailing a peace process that has yet to materialize.

“I heard a lot of noise about the idea of bolting but not from people who are as close as you would expect to the decision-making circles,” said Ghassan Khatib, a Palestinian political scientist at Birzeit University in the West Bank. But he said, “sooner or later the Palestinians are going to realize there is nothing new, and they will go back to acting in the international arena.”

Mr. Greenblatt declined to say whether he had presented a plan or whether he had given the Palestinians any comfort on the two-state solution, which Mr. Trump threw into doubt last February when he said, “I’m looking at two-state and one-state” formulations.