Josh Raffel, a White House spokesman, said the administration was still working on its plan, “which is designed to benefit both the Israeli and Palestinian people.”
“We will present it when it is done and the time is right,” he said in a statement.
Mr. Kushner and Mr. Greenblatt left the public statements on Tuesday to Nikki R. Haley, the American ambassador to the United Nations, who once again defended the administration’s decision last year to move the United States Embassy from Tel Aviv to Jerusalem.
The decision, which was one of Mr. Trump’s central campaign promises, reversed decades of diplomatic practice and was widely condemned internationally even by key American allies.
For the Palestinians, it has undermined the impartiality of the United States as a negotiating partner, a role that has been central to the foreign policy of successive American administrations. The Palestinians have long sought to establish East Jerusalem as the capital of a Palestinian state, and the decision to move the embassy, along with Mr. Trump’s declaration last month that the status of Jerusalem was “off the table,” has been seen by many Palestinians as precluding that possibility.
Though Mr. Abbas called the decision “dangerous and unprecedented” on Tuesday, he notably did not call for the United States to be excluded from negotiations. Rather he proposed the creation of a “multilateral international mechanism” and the inclusion of other partners in the process. He did not elaborate, though he mentioned a willingness to take up a Russian proposal to hold peace talks in Moscow.
His remarks were met with booming applause in the Security Council chamber. François Delattre, France’s ambassador, praised what he called Mr. Abbas’s “courageous commitment” to peace and said France was open to studying his proposals.
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Mr. Danon, Israel’s ambassador, did not share that assessment, accusing Mr. Abbas, who left the chamber immediately after speaking, of running away from negotiations.
“Rather than driving just 12 minutes between Ramallah to Jerusalem, he has chosen to fly 12 hours to New York to avoid the possibility of peace,” Mr. Danon said.
Noting that there were other pressing concerns in the Middle East, like the civil wars in Yemen and Syria, Ms. Haley accused the United Nations of having a distracting fixation on the Israeli-Palestinian conflict. “The U.N.’s disproportionate focus has actually made the problem more difficult to solve, by elevating the tensions and the grievances between the two parties,” she said.
The acrimonious back and forth played out amid continuing turmoil in the region. In Israel, the police have recommended that bribery and fraud charges be filed against Prime Minister Benjamin Netanyahu, with unpredictable consequences for the peace process.
And in Gaza, home to two million Palestinians, a continuing political standoff between Hamas, the Islamist militant group, and the secular Fatah party is leading to a “humanitarian, economic and ecological calamity,” according to Nikolay Mladenov, the United Nations special coordinator for the Middle East peace process.
Speaking at the start of Tuesday’s Security Council session, Mr. Mladenov presented a grim assessment of the region, where he said “the enemies of peace are growing more confident by the day.”
“Our window of opportunity is closing,” he said, “and if we do not seize it quickly, the Israeli-Palestinian conflict will be engulfed in the whirlwind of religious radicalization that remains present in the region.”