The president’s message was all the more striking given how little Mr. Netanyahu’s coalition government supports any major initiative with the Palestinians, particularly one that would involve two states, one for Israelis, one for Palestinians.

Isaac Herzog, the head of the Labor Party and the opposition, who spoke with Mr. Trump in a receiving line at an airport arrival ceremony, said he was struck by how central the president made the Palestinian issue and that he tied it to Saudi Arabia and to Israel’s other Arab neighbors.

“The regional opportunity is ready and ripe,” Mr. Herzog said in an interview. “I was very pleased as one who leads the Israeli opposition and the peace camp in Israel. We were very pleased that the president showed he is trying to break the impasse.”

Mr. Trump’s remarks set the tone for a busy two days of peacemaking and symbolism. After meeting with Mr. Rivlin, the president visited the Church of the Holy Sepulcher, home of what is believed to be the tomb of Jesus Christ, and then the Western Wall, the holiest site for Jewish prayer, where he donned the traditional skullcap and left a note in a crevice. He planned to meet and then dine with Mr. Netanyahu later in the evening.

On Tuesday, Mr. Trump is to travel the short distance to Bethlehem, in the West Bank, to meet with President Mahmoud Abbas of the Palestinian Authority. Mr. Trump is then scheduled to return to Jerusalem to lay a wreath at Yad Vashem, the holocaust remembrance center, and to deliver a speech at the Israel Museum.

Mr. Trump arrived on what was believed to be the first open, direct flight to Israel from Saudi Arabia, which do not have diplomatic relations, a sign of the possibility he sees for what he has called “the ultimate deal.” In wading into Middle East peacemaking, Mr. Trump will test whether a lifetime of business deal making can be translated into progress in the world of international diplomacy.

“We have before us a rare opportunity to bring security and stability and peace to this region and its people, defeating terrorism and creating a future of harmony, prosperity and peace,” Mr. Trump said during an arrival ceremony at Ben-Gurion International Airport outside Tel Aviv before flying by helicopter to Jerusalem. “But we can only get there working together. There is no other way.”

President Trump, center, with Prime Minister Benjamin Netanyahu, right, and President Reuven Rivlin of Israel. CreditJim Hollander/European Pressphoto Agency

Mr. Netanyahu repeated his longstanding position that he “shares the commitment to peace” but with the same conditions as always. “Israel’s hand is extended in peace to all our neighbors, including the Palestinians,” he said. “The peace we seek is a genuine and durable one, in which the Israeli state is recognized, security remains in Israel’s hands, and the conflict ends once and for all.”

No previous American president has come to Israel this early in his tenure. Bill Clinton visited in his second year in office and Jimmy Carter in his third, while Richard M. Nixon, George W. Bush and Barack Obama all waited until their second terms to make the trip. American flags flew in Jerusalem, and Jewish and Christian holy sites prepared to host Mr. Trump, his wife, his daughter and his son-in-law.

But there were clashes in the West Bank as Mr. Trump arrived. More than 1,000 Palestinians marched to the Qalandiya checkpoint from Ramallah, carrying posters of Palestinian prisoners on hunger strike in Israeli prisons. Some carried pictures of Mr. Trump’s face with a red shoe print that read, in Arabic: “American policies are a footprint of shame on humanity’s forehead. Trump’s visit is a sale of disillusionment and a station to bypass Palestinian rights.”

When the demonstration reached the checkpoint, Israeli soldiers began firing tear-gas canisters, rubber bullets and live ammunition and about 50 Palestinian youths clashed with the soldiers.

Mr. Trump at a bilateral meeting with Mr. Rivlin in Jerusalem. CreditStephen Crowley/The New York Times

Secretary of State Rex W. Tillerson told reporters aboard Air Force One that he saw an opening to succeed where multiple presidents have failed.

“We have the opportunity to advance the peace discussions between the Israelis and the Palestinians,” he said. “I think the president has indicated he’s willing to put his own personal efforts into this if the Israelis and the Palestinian leadership are ready to be serious about engaging, as well.”

But a visit that was once anticipated as a powerful expression of solidarity between two like-minded leaders, Mr. Trump and Mr. Netanyahu, has become more complicated amid a series of logistical and political stress points.

Although Mr. Trump presented himself during last year’s campaign as the staunchest ally Israel could hope for in the White House, since taking office, he has backed away from some of his promises and adopted an approach closer to that of his predecessors.

Mr. Trump and his wife, Melania, visiting the Church of the Holy Sepulcher in Jerusalem on Monday.CreditStephen Crowley/The New York Times

Israelis had expected the United States to have announced by now plans to move its embassy to Jerusalem from Tel Aviv, as Mr. Trump had vowed to do “quickly.” But the American president has postponed that promise because of fears that it could provoke a backlash among Palestinians and their Arab allies, complicating peace negotiations. Mr. Trump’s full-throated defense of Israeli settlements has also evolved into a request that Mr. Netanyahu delay new projects.

The days leading up to Mr. Trump’s arrival underscored the potential for friction. Mr. Trump disclosed to Russia’s foreign minister and its ambassador to Washington last week classified information about an Islamic State plot that had originally come from Israel, potentially jeopardizing the Israeli intelligence source. American officials also declined to invite Mr. Netanyahu to accompany Mr. Trump to the Western Wall and would not say that the sacred site was part of Israel, actions that made many Israelis bristle.

The $110 billion in arms sales that Mr. Trump announced in Saudi Arabia before arriving was also a source of concern. Mr. Netanyahu had to order cabinet ministers to go to the arrival ceremony at the airport, after some had said they would not attend. Some Israeli officials said their main hope for the visit was to make sure that there was no great gaffe or misunderstanding.

Mr. Tillerson said the arms sales to the Saudis should not concern the Israelis. “There has been nothing entered into with the arms sales agreements with the kingdom of Saudi Arabia or any of the other countries that do not fully allow us to fulfill our commitments to Israel and the longstanding security arrangements we have with Israel,” he said. “I’m sure we can answer those questions and address the concerns they have.”

Mr. Trump at the Western Wall. CreditStephen Crowley/The New York Times

Mr. Netanyahu has resolved not to mention the intelligence breach publicly, but Israeli officials and intelligence officers have privately expressed anger and frustration. Mr. Tillerson said the president had no need to express regret. “I don’t know that there’s anything to apologize for,” he said. “To the extent the Israelis have any questions, or clarification, I’m sure we’re happy to provide that.”

Despite all that, much as he was in Saudi Arabia, Mr. Trump is viewed by many in Israel as a welcome change from Mr. Obama, whose relationship with Mr. Netanyahu soured early on, after Mr. Obama called for a settlement freeze, and only worsened from there.

Mr. Obama’s support for an agreement intended to curb Iran’s nuclear program was also seen by many in Israel as a fundamentally bad deal, a view that Mr. Trump says he shares.

Mr. Trump arrived just a couple of weeks shy of the 50th anniversary of the Arab-Israeli war of 1967 when, among other territorial gains, Israel annexed East Jerusalem and occupied the West Bank, as it does to this day.

Until Mr. Trump, recent American presidents had said that any final resolution of the dispute would end with the creation of a Palestinian state that could exist side by side with Israel. But Mr. Trump has abandoned that assumption, saying that he would be happy with any solution that satisfied the two sides.

Mr. Netanyahu, who has staked much on his relationship with Mr. Trump, seemed intent on erasing any doubts about their fledgling friendship, offering what he called a “very warm welcome” at the airport and calling the American president “Don” and “Donald.” Mr. Trump, for his part, appeared happy to see Mr. Netanyahu.

“Hello, my friend,” Mr. Trump said when he stepped onto the tarmac.

“Welcome, our good friend,” Mr. Netanyahu responded with relish.