“I’d like to see you hold back on settlements for a little bit,” Mr. Trump told Mr. Netanyahu on Feb. 15, during the Israeli premier’s visit to the White House. “We’ll work something out.”
Mr. Netanyahu replied, “Let’s try it,” prompting Mr. Trump to joke, “Doesn’t sound too optimistic, but he’s a good negotiator.”
On Thursday, a delegation of senior aides to Mr. Netanyahu left Washington after four days of talks with a White House team that left the settlements issue unresolved. A White House statement said administration officials had reiterated Mr. Trump’s “concerns” about the impact of new settlements on the prospects for peace.
But the statement added that the “Israeli delegation made clear that Israel’s intent going forward is to adopt a policy regarding settlement activity that takes those concerns into consideration.”
Mr. Trump surprised virtually everybody when he raised Israeli settlements as an issue after taking office. Many in Israel expected that, given his unstinting support of Mr. Netanyahu during the campaign and his vow to move the American Embassy from Tel Aviv to Jerusalem, he would give the Israelis carte blanche to expand settlement construction.
Instead, the administration put the embassy move on the back burner. And Mr. Trump told an Israeli newspaper, Israel Hayom, that he viewed settlements as unhelpful for a peace accord. “Every time you take land for settlements,” he said, “there is less land left.”
The last time Mr. Netanyahu tangled with a president over settlements, the dispute played out publicly: President Barack Obama’s secretary of state, Hillary Clinton, demanded that Israel cease all construction — “not some settlements, not outposts, not natural-growth exceptions.” This time, the two sides appear determined to work out an understanding privately, so as not to undermine the rapport the two leaders have established.
Extracting a deal from Mr. Netanyahu in current circumstances would be tricky. The Israeli leader is politically more vulnerable than he was eight years ago, when Mr. Obama demanded that he freeze all construction.
Right-wing members of his coalition are committed to the settler movement and Mr. Netanyahu, several experts said, cannot afford to look as if he is yielding too quickly to Mr. Trump’s pressure.
“He can’t square the circle,” said Martin S. Indyk, who served as special envoy for Israeli-Palestinian negotiations during the Obama administration. “He can’t agree to a freeze and keep his coalition.”
But Mr. Netanyahu, experts said, could also use his new rapport with Mr. Trump to his advantage. The standoff over settlements helped poison Mr. Netanyahu’s relationship with Mr. Obama, and the Israeli leader can argue that it must not be allowed to do the same with Mr. Trump.
“I don’t think you can come to a quick deal,” said Dennis B. Ross, who also advised Mr. Obama and several other presidents on the peace process. “It looks like there is a context being created for an agreement later on.”
Previous administrations have struggled in their attempts to negotiate deals on settlements. The Obama administration managed to get Mr. Netanyahu to agree to a 10-month moratorium on construction, which was meant to open a window for talks between Israel and the Palestinians. But the 2010 process went nowhere, in part because the Palestinians did not come to the table until the moratorium was close to expiring, and Mr. Netanyahu refused to extend it.
Mr. Trump has named a longtime lawyer from his real estate company, Jason D. Greenblatt, to lead the negotiations with Israel. Mr. Greenblatt reports to Jared Kushner, Mr. Trump’s son-in-law, who did not take part in this week’s negotiations. Mr. Greenblatt has tasked a National Security Council official from the Obama administration, Yael Lempert, to help in the talks, which has fanned criticism from the right wing in Israel.
“These guys are learning on the run,” said Daniel C. Kurtzer, a former American ambassador to Israel and Egypt. “They’re also understanding that you can get snookered here.”
Mr. Kurtzer, who was involved during the George W. Bush administration in trying to set specific limits to settlement construction, said the process was bewildering in its complexity. Defining settlement blocs, and defining permissible construction within them, is open to endless debate, he said.
Settlements have become increasingly contentious at the United Nations as well. It is arguably the most politically delicate issue for the new secretary general, António Guterres, as he seeks to create a working relationship with the Trump administration, which has accused the organization of a deep anti-Israel bias.
Anything that the administration considers hostile to Israel, Mr. Guterres knows, could be used to alienate both the White House and influential members of Congress who exert enormous influence over American financial support for the 193-member United Nations.
The Security Council voted in a Dec. 23 resolution to condemn the Israeli settlements as illegal and demand that Israel halt their construction, arguing they constituted a major obstacle to peace talks. Mr. Trump, president-elect at the time, expressed fury at the Obama administration for having abstained in that vote instead of blocking it with a veto.
At the Security Council on Friday, the secretary general’s special envoy for the Middle East, Nickolay Mladenov, said in his first report since the resolution was adopted that Israel not only had failed to comply with the demand on settlements, but had undertaken a big expansion, of more than 5,000 units. Mr. Mladenov called the expansion “deeply concerning” and said that the “territorial contiguity of a future Palestinian state” is threatened.
“Such actions are in breach of international law and they must stop,” Mr. Mladenov said. “Settlement expansion undermines the very essence of a two-state solution.”