Certainly, Mr. Trump is not missing chances to press his case. Aides recount, for example, that last month, when he reached Treasury Secretary Steven Mnuchin on his cellphone in Davos, Switzerland, Mr. Mnuchin relayed that he was in a meeting with King Abdullah II of Jordan. Mr. Trump requested to speak to the king, whom he then asked for help in dealing with the aggrieved president of the Palestinian Authority, Mahmoud Abbas.
There are no signs that Mr. Abbas is softening. The Palestinians broke ties with the administration in December, after Mr. Trump recognized Jerusalem as the capital and announced plans to move the American Embassy from Tel Aviv. They complained bitterly that the United States had forfeited its role as a credible broker between them and the Israelis.
Their fury only deepened when Mr. Trump declared last month at a meeting with Mr. Netanyahu that he had taken Jerusalem “off the table.” Palestinians have long aspired to have East Jerusalem as the capital of a Palestinian state. Mr. Abbas set off on a tour of world capitals, including Moscow, to see whether he could find another leader for the peace process.
Administration officials said they were confident that the Palestinians would recognize their lack of options and return to the fold eventually. But after swinging so heavily toward Israel, they also seem to realize the need to restore a semblance of balance to the statements made by administration officials.
Mr. Trump’s tone first changed on Sunday, when he told a right-wing Israeli newspaper, Israel Hayom, that he was concerned about the growth of Jewish settlements on the West Bank. “Settlements,” he said, “are something that very much complicates and always have complicated making peace.”
Asked what he meant by “taking Jerusalem off the table,” the president said, “Jerusalem is the capital of Israel, and as for specific boundaries, I would support what both sides agreed to” — language drafted by Mr. Greenblatt to keep open at least the veneer of a negotiated settlement.
While Mr. Trump criticized the Palestinians for “not looking to make peace,” he added, “I am not necessarily sure that Israel is looking to make peace.”
Mr. Trump has issued statements like those before, but officials noted that in this case, he was making them to a Hebrew-language paper read by the Israeli right. Among the paper’s key investors is Sheldon G. Adelson, the Las Vegas casino magnate who is one of Mr. Trump’s biggest donors and a driving force behind the Jerusalem decision.
“They have some messages that need to be delivered to the Israeli side,” said Daniel B. Shapiro, who served as Barack Obama’s ambassador to Israel. “It may presage that the president means what he says: that he would expect Israel to put some chips on the table.”
On Monday, after reports in the Israeli news media that Mr. Netanyahu had told members of his Likud Party that he had discussed with the United States a plan for Israel to annex territory in the West Bank, the White House gave an unusually blunt denial.
“The United States and Israel have never discussed such a proposal,” said a White House spokesman, Josh Raffel, “and the president’s focus remains squarely on his Israeli-Palestinian peace initiative.”
Analysts said Mr. Netanyahu’s reference to talks with the United States reflected his legal troubles. He was trying to head off legislation annexing West Bank territory. But he was also trying to shore up support among hard-line members of his party in advance of the recommendation that he be charged with bribery, fraud and breach of trust.
How those legal travails will affect Mr. Netanyahu’s approach to a peace deal is hard to predict, analysts said, though some said they expected the prime minister to emphasize security issues over peacemaking for the next few months — a strategy that could lead to further friction with Mr. Trump.
“The rebuke of Bibi is quite unprecedented in the annals of the Trump-Bibi relationship,” said Martin S. Indyk, who was Bill Clinton’s ambassador to Israel, using Mr. Netanyahu’s nickname. “This is about their desire to preserve their credibility for the peace process, having damaged it so much with the Jerusalem announcement.”
Still, analysts said the White House would need more than a few sharp-edged statements toward Israel to persuade the Palestinians that the process was not stacked against them. In private, administration officials are scathing about Mr. Abbas and the Palestinian leadership.
The Palestinian Authority faces other potential blows in Washington, like a congressional cutoff of American economic aid because of its funding of terrorism and the closing of the Palestine Liberation Organization’s office in the capital.
The United States is working with Saudi Arabia and other Arab countries to line up hundreds of millions of dollars in financial support for the Palestinians. But even that might not prove sufficient to persuade them to sign Mr. Trump’s deal.
“They’ve so dug themselves in on Jerusalem,” said Aaron David Miller, a former Middle East negotiator. “They’re going to have to figure out how to give the Palestinians more than 20 cents on the dollar.”