JERUSALEM — President Trump told Israelis and Palestinians on Tuesday that he knows they are eager to reach a peace agreement with each other and that he is committed to helping them “make a deal.”

In a speech at the Israel Museum as he prepared to end his four-day trip to the Middle East and depart for his next stop in Rome, Trump repeated his call for Arab countries and Israel to form a grand coalition with the United States to “drive out the terrorists and the extremists from our midst” and “defend our citizens and the people of the world.”

“This trip is focused on that goal,” he said.

Trump recognized that Israeli-Palestinian peace is a key component of cooperation in the region, although he has not outlined how he hopes to achieve an agreement that has eluded many presidents before him.

In some respects, his effusive praise for Israel during his two days here — which also included a Tuesday morning visit to Palestinian Authority President Mahmoud Abbas in Bethlehem, in the Israeli-occupied West Bank — appeared to endorse Israeli claims to a united capital in Jerusalem.

Noting that Jerusalem is a “sacred city,” and that “the ties of the Jewish people to this holy land are ancient and eternal,” Trump recalled his Monday visits to the Western Wall and the Church of the Holy Sepulchre, sites sacred to Jews and Christians in East Jerusalem, part of the West Bank, and claimed by Palestinians as the capital of their envisioned state.

To sustained applause, Trump cited the “unbreakable bond” between the United States and Israel, a place he called “a testament to the unbreakable spirit of the Jewish people.” He spoke of “a future where Jewish, Christian and Muslim children can grow up together in peace.”

“America’s security partnership with Israel is stronger than ever,” he said. “Under my administration, you see the difference. Big, big beautiful difference, including the Iron Dome missile defense program . . . [and] David’s Sling,” an aircraft interception system. The former was established here under the Obama administration, the latter under President George W. Bush.

Israeli Prime Minister Benjamin Netanyahu and Trump, who introduced him and praised “the leadership that you bring,” condemned Monday night’s terrorist attack in Britain, claimed by the Islamic State.

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But in describing the authors of global terrorism, Trump focused nearly all his attention on Iran and the anti-Israel organizations it supports, Hezbollah and Hamas. Iran’s leaders, he said, “routinely call for Israel’s destruction. Not with Donald J. Trump,” he said. “Believe me.”

“The United States is firmly committed to keep Iran from developing a nuclear weapon and halting their support of terrorism and militias,” Trump said to sustained applause as Netanyahu stood and pumped his fist.

The audience included U.S. and Israeli officials, as well as prominent citizens from both. Las Vegas casino mogul Sheldon Adelson and his wife, Miriam, who donated millions of dollars to support Trump’s campaign and then his inauguration, were seated just behind the stage, near first lady Melania Trump and Secretary of State Rex Tillerson.

Before his speech, Trump and his delegation visited the World Holocaust Remembrance Center at Yad Vashem, where he said the Jewish people had built the state of Israel out of the “depths of suffering” as “a testament to [their] unbreakable spirit.”

Earlier, he had traveled to Bethlehem for a private meeting with Abbas to discuss the peace process and his vision for anti-terrorism cooperation.

In joint remarks afterward, Abbas said he welcomed Trump’s efforts, which had “given all the nations across the region so much hope and optimism of the possibility of making a dream come true.”

“Our commitment is to cooperate with you in order to make peace and forge a historic peace deal with the Israelis,” Abbas added.

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But while Trump spoke in generalities about the goal, Abbas laid out the specifics of Palestinian demands — which have been supported by the Arabs and rejected by Israel through decades of unsuccessful peace negotiations shepherded by American presidents.

“We reassert to you our positions of a two-state solution along the borders of 1967, a state of Palestine with its capital in East Jerusalem, living alongside of Israel,” he said, referring to Israel’s occupation of the West Bank following a war against three Arab armies.

During the presidential campaign, Trump pledged to move the U.S. Embassy from Tel Aviv to Jerusalem, but the plan has been shelved, at least temporarily.

Abbas said he had also drawn Trump’s attention to more than 1,000 Palestinian prisoners held by Israel who have been on a hunger strike for over a month, led by Marwan Barghouti, whom supporters call the Palestinian Nelson Mandela.

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Abbas delivered to Trump a letter from the families of the strikers, who have demanded more family visits, access to telephones, medical care, the freedom to study and cessation of isolation as a punishment.

Israel and some U.S. lawmakers have objected to American aid to the Palestinians, claiming the money is used to make payments to the families of prisoners, who are considered “freedom fighters” among many Palestinians. Trump did not mention the aid or the payments in his public remarks.

Abbas also spoke of Palestinian insistence that all “final status issues” be resolved “based on international law” and United Nations resolutions, as well as the Arab Peace Initiative first offered more than a decade ago. It promised Arab recognition of Israel in exchange for a Palestinian state.

Escorted by Israeli police and helicopters, Trump and his delegation sped down Hebron Road and found themselves, just minutes from their Jerusalem hotel, at the gates of Bethlehem in the West Bank.

The closeness of Bethlehem — the physical proximity between Israel and the Palestinian territory — surprised most first-time visitors in the entourage.

Trump and the convoy passed through the 26-foot-tall concrete wall with watch towers that is Israel’s barrier and past “Checkpoint 300,” where thousands of Palestinian workers cross into Israel each morning to reach their jobs on construction sites.

Trump has cited the Israeli barrier as an example of the kind of wall he wants to build between the United States and Mexico, but many Palestinians view it as a symbol of oppression.

Bethlehem is lively and crowded, home to Palestinian Muslims and Christians and the Church of the Nativity, the Byzantine-era sacred site built over the grotto where the faithful believe Jesus was born.

The city is also surrounded by hilltop Jewish settlements on three sides, built in East Jerusalem and the West Bank, communities that most of the world considers illegal, though Israel disputes this.

Later, Trump told his museum audience that after his meeting with Abbas, “I can tell you the Palestinians are ready to reach for peace … I know you’ve heard it before. I’m telling you, they are ready to reach for peace.

“My good friend Benjamin [Netanyahu], he wants peace.” Both sides, he said, “will face tough decisions. But with determination and compromise … Israelis and Palestinians can make a deal.”

There was no applause from the audience.