JERUSALEM — As President Trump appeared to shift closer to the political center on several contentious policies on Israel, Prime Minister Benjamin Netanyahu suggested on Sunday that it was unrealistic to expect their two countries to agree completely on all issues.
But amid growing challenges from the right, Mr. Netanyahu said he was the strongest leader to navigate the relationship — the nation’s most important, yet often its trickiest.
The Israeli leader’s comments came the night before he leaves for Washington for his first face-to-face meeting with Mr. Trump as president.
While Mr. Trump at first appeared to give Israel’s leaders carte blanche — he remained silent, for example, as the nation announced the construction of thousands of new homes in the occupied West Bank — he has since said he does not believe that “going forward with these settlements is a good thing for peace.”
And on Sunday, Mr. Netanyahu was quoted on Army Radio telling members of his right-wing Likud Party that “to believe there are no restrictions now would be a mistake.”
The meeting with Mr. Trump on Wednesday is expected to set the tone for the American-Israeli relationship, which was notably frosty under President Barack Obama because of Israeli settlements in occupied territory, Israel’s vehement opposition to the nuclear deal with Iran and personality clashes with Mr. Netanyahu.
Although Mr. Trump’s comments on the settlements have tamped down expectations on the right of a new era unfettered by American constraints, some analysts here portray the president’s position as politically beneficial to Mr. Netanyahu. He is portraying himself as an experienced hand in dealing with Washington — unlike, he suggested, more aggressive forces on the right who are suggesting an annexation of some settlements.
“I have navigated Israeli-U.S. relations in a prudent manner, and I will continue to do so now,” he told cabinet members on Sunday, according to an official transcript of his remarks, in which he noted that he and Mr. Trump “have known each other for years.”
His main rival to the right, Naftali Bennett, the Jewish Home Party leader and education minister, warned Mr. Netanyahu not to discuss the possibility of a state for Palestinians — though Mr. Netanyahu has tepidly endorsed one and Mr. Trump has said repeatedly that he would like to make an unspecified “deal” for peace between Israelis and Palestinians.
“If in their statements after the meeting they mention, for the first time in Trump’s term, their obligation to forming Palestine or two states in one way or another, we will all feel it in our flesh for years to come,” Mr. Bennett warned in a Facebook post. “The earth will shake.”
The tussle between the two men is personal — Mr. Bennett would like to succeed Mr. Netanyahu as prime minister — and central to the longstanding conflict here: Mr. Bennett argues that the time for a separate state for Palestinians is over and that Israel has an opportunity under Mr. Trump to significantly expand Jewish presence in the West Bank.
Apart from the challenge from the right, the meeting comes at a difficult time for Mr. Netanyahu, as he faces at least three investigations into allegations of corruption.
Mr. Trump has also backed off, for now at least, a campaign promise to relocate the United States Embassy to Jerusalem from Tel Aviv, a move opposed by the Palestinians, who would consider it a de facto recognition of Israel’s annexation of East Jerusalem after the 1967 war.
Here again, political analysts have seen Mr. Netanyahu’s influence, with the prime minister possibly communicating that such a move was not a top priority given the reaction it could provoke among Palestinians.
In his statements on Sunday, Mr. Netanyahu also said he had registered his opposition to appointing the well-regarded former Palestinian prime minister, Salam Fayyad, as the United Nations envoy to Libya.
On Friday, the new American ambassador to the United Nations, Nikki R. Haley, opposed the appointment. “For too long, the U.N. has been unfairly biased in favor of the Palestinian Authority to the detriment of our allies in Israel,” she said.
The Israeli news media also reported over the weekend that Tzipi Livni, a prominent Israeli lawmaker, may be offered a position as an under secretary-general for the United Nations chief, António Guterres.