At the same time, the Palestinian Authority president, Mahmoud Abbas, generally seen as hesitant, or even obstructionist, may to Mr. Trump seem the most accommodating.
It is at once a case study in why this region is so unpredictable and a test of whether the new president is in over his head or knows something his many failed predecessors did not.
“We are close allies and share the same worldview,” Shuli Moalem-Refaeli, a member of the Knesset in the Jewish Home party, said of Mr. Trump. But she urged Mr. Netanyahu, whose party is a coalition partner with hers, not to discuss two states even if Mr. Trump pushes that as a solution.
“I pray that the process with the U.S. administration will not come to any harm to our close relations,” she added. “I hope we will continue to have good relations, even if we don’t agree.”
Israeli officials are keeping remarkably silent on the intelligence breach with the Russians, so it is difficult to tell whether it has hurt Mr. Trump’s position with Israel. Some experts speculate that the new tension may make Mr. Trump more likely to fulfill an Israeli dream: having the United States move its embassy to Jerusalem, tacitly supporting Israel’s claim that the divided city is its eternal capital.
But at this point, no one expects huge progress in Mr. Trump’s quick trip, which has already been tangled in diplomatic stumbles. In one, a scheduled trip to Masada, where Mr. Trump wanted to deliver a speech at the Roman-era mountaintop retreat that stands as a symbol of Israel’s unwillingness to surrender, was called off during the hubbub on Tuesday.
Feelings here were deeply wounded when American officials declined to allow Israeli leaders, Mr. Netanyahu among them, to accompany Mr. Trump on the first visit of a sitting American president to the Western Wall. (The United States and most other nations have not recognized Israel’s annexation of East Jerusalem after the 1967 war, thus it remains, in policy, occupied land.)
All of this, mixed with a slowly building apprehension here that Mr. Trump might not, after all, be in the mood to give the Israeli right everything it wants, has left the distinct appearance that Mr. Netanyahu will be on the defensive as the American president arrives. The two leaders took pains on Tuesday to reassert their working relationship in a phone call, but some chill is likely to last.
On the Palestinian side, meanwhile, there is little to lose in being solicitous to Mr. Trump.
Mr. Abbas’s advisers say that meetings with Mr. Trump’s team here and in Washington have been highly productive, and that Mr. Abbas, 82, wishes to be the Palestinian leader who finally makes a deal. Critics note that he is highly unpopular at home and his survival depends on maintaining power. Thus he has few options other than to restart talks if that is what Mr. Trump and regional Arab leaders want.
“What we want is a state of our own to live side by side with Israel,” said Majdi al-Khalidi, Mr. Abbas’s diplomatic adviser.
David Keyes, Mr. Netanyahu’s spokesman, said that the prime minister has “consistently” called on Mr. Abbas to negotiate but has repeatedly been turned down. “No external pressure is required for him to begin negotiations and no domestic pressure will prevent him from doing so,” Mr. Keyes said in a statement.
“It requires some chutzpah for President Abbas to say he educates Palestinian children ‘on a culture of peace’ when he names public squares, schools, and sports clubs for mass-murders and pays convicted terrorists hundreds of millions of dollars each year,” he said. “Prime Minister Netanyahu will be the first to welcome a genuine change in these Palestinian policies.”
The Israeli government’s rising tension with Mr. Trump is a departure from the mood here in the days after his election, which the Israeli right celebrated with vigor after eight tumultuous years with President Barack Obama. Mr. Trump had promised to move the American Embassy to Jerusalem, a step other nations have not taken, and he remained silent as the right announced renewed settlement building and even possible annexation in the West Bank.
There is much less fervor now. Mr. Trump decided not to move the embassy immediately, out of fear of backlash among Palestinians and the Arab world. He also publicly asked Mr. Netanyahu to exercise restraint on Jewish settlement in the West Bank, which would mean less land for a possible Palestinian homeland.
While Mr. Trump’s national security adviser, Lt. Gen. H.R. McMaster, said last week that the president intended to “reaffirm America’s unshakable bond to the Jewish state,” he also said he would “express his desire for dignity and self-determination for the Palestinians.” This has made many of Mr. Netanyahu’s allies nervous.
The embassy move remains an issue. Secretary of State Rex W. Tillerson, who will be traveling with the president here, has said that no final decision has been made, and that the administration is still mulling “what impact such a move would have” on peace talks.
Mr. Trump has until June 1 to decide: United States law calls for such a move, but his predecessors, concerned about reaction in the Arab world, signed waivers delaying the move every six months. (Mr. Tillerson also ruffled feathers here by referring to “Palestine,” a name Israel sees, and rejects, as a recognition of a Palestinian state.)
In what the Israeli media declared on Monday was the “first” disagreement with Mr. Trump about this visit — suggesting more to come, and they did — Mr. Netanyahu quickly answered Mr. Tillerson by saying that moving the embassy would only advance peace “by shattering the Palestinian fantasy according to which Jerusalem isn’t the capital of Israel.”
Though Mr. Abbas has opposed such a move as a de facto recognition of Israeli sovereignty over all of Jerusalem — the Palestinians demand East Jerusalem as their future capital — he has been mostly mum on the issue these days.
Reaction in Israel to Mr. Trump’s information sharing with Russia was uncharacteristically muted, with most outlets sticking to citing foreign media reports. It did not appear that any office-holding politician commented on it, and other analysts did so with the greatest of caution. One paper, Israel Hayom, mentioned the story only on page 7. (The paper is partially owned by Mr. Trump’s patron, the casino billionaire Sheldon Adelson.)
Instead, a juicy subplot has captured the Israeli media: Ronald S. Lauder, the American businessman and president of the World Jewish Congress, has been speaking with Mr. Abbas as well as with his friend Mr. Trump. Mr. Lauder and Mr. Netanyahu, long friends, have fallen out in recent years, and Mr. Netanyahu was quoted in The Jerusalem Post this week as calling Mr. Lauder his “biggest obstacle” in the coming decisions with Mr. Trump. Mr. Lauder’s spokesman declined to comment.
Among the most pressing questions, though, is whether any of the men, Mr. Trump, Mr. Abbas or Mr. Netanyahu, are capable of reaching deals that escaped the likes of Yitzhak Rabin and Bill Clinton, to name but a few.
“Most Palestinians have lost trust in Mahmoud Abbas’s ability to reach a fair and just deal,” said Fadi Quran, a young Palestinian activist and senior campaigner at Avaaz, a liberal advocacy group.
Oded Revivi, the mayor of the Jewish settlement Efrat who attended Mr. Trump’s inauguration and has met with his envoy here, has been one of the most prominent voices in arguing that two states is a failed enterprise. He asked: “Can any of the three deliver? Does any of them have enough support?”
Gilead Sher, a former Israeli negotiator under Prime Minister Ehud Barak and now a senior fellow with the Institute for National Security Studies in Tel Aviv, said an almost incalculable number of variables would have to fall in place.
Mr. Netanyahu, he said, could re-form his government with politicians who support a deal, such as those from the Labor Party. And, he said, Mr. Trump would have to be able to get regional Arab players — Egypt, Saudi Arabia, Jordan and the United Arab Emirates — on board as well as restart talks directly between Israelis and Palestinians.
And Mr. Trump himself?
“He’s so unpredictable you cannot know what he will do,” he said. “It’s quite odd, but he might be the man to do it.”