President Donald Trump said Tuesday he is hopeful the United States can help forge peace between Israel and the Palestinians, adding that he believes such an agreement would "begin a process of peace all throughout the Middle East."
Speaking alongside Palestinian President Mahmoud Abbas in Bethlehem, Trump said he is committed to doing everything he can to achieve a deal.
"President Abbas assures me he is ready to work toward that goal in good faith, and Prime Minister [Benjamin] Netanyahu has promised the same. I look forward to working with these leaders toward a lasting peace," Trump said.
Abbas said he also has hopes for a peace deal, and is ready to be a partner in what he called a "noble" mission.
The last Israeli-Palestinian peace talks broke down in 2014.
Trump's schedule Tuesday also includes a visit to the Holocaust memorial Yad Vashem and a speech.
He met Monday with Netanyahu, and drew quick approval as he assailed Iranian aggression and military ambitions.
Trump also attacked the administration of former U.S. President Barack Obama for agreeing to the 2015 international deal restraining Iran's nuclear weapons program in exchange for lifting economic sanctions against Tehran, a pact the Jewish state adamantly, but unsuccessfully, opposed.
"I want you to know how much we appreciate the change in American policy on Iran," Netanyahu told Trump at the end of a day of meetings and ceremony. "I want want to tell you also how much we appreciate the reassertion of American leadership in the Middle East."
Trump attacked Iran throughout the day, saying, "Instead of being thankful, saying thank you" for the nuclear deal, Iranians "now feel emboldened," with signs of Tehran's fighters, money and weapons in Yemen, Iraq and Syria. "We not only gave them a lifeline, we gave them wealth and prosperity. It was a terrible thing for the United States to enter into that deal."
WATCH: Trump's comment about Iran during remarks in Jerusalem
Before private talks with the Israeli leader, Trump also took the occasion to deny that when he was meeting with top Russian diplomats in Washington earlier this month he had unmasked Israel as the U.S.'s clandestine source for highly classified information about a potential Islamic State airplane terrorist attack.
"Just so you understand, I never mentioned the word or the name Israel, never mentioned it in that conversation," Trump said. "They were all saying I did, so you had another story wrong. Never mentioned the word Israel.” News accounts of the White House conversation said that Trump had mentioned enough information that Russia would be able to figure out the source for the covert information, which later was revealed as coming from Israel.
Earlier, Trump said, "This moment in history calls us to strengthen our cooperation as both Israel and America face common threats from ISIS and other terrorist groups to countries like Iran that sponsor terrorism and fund and foment terrible violence - not only here - but all over the world.
"Most importantly," he added, "the United States and Israel can declare with one voice that Iran must never be allowed to possess a nuclear weapon - never ever - and must cease its deadly funding, training and equipping of terrorists and militias. And it must cease -- immediately."
Trump met with Israeli President Reuven Rivlin ahead of his talks with Netanyahu and visited important symbols of both the Jewish and Christian faiths.
The U.S. president arrived in Israel after a two-day visit to Saudi Arabia, where Trump said King Salman assured him the Saudis want peace between the Israelis and Palestinians and roadblocks imposed against Iranian threats.
"There is a growing realization among your Arab neighbors that they have common cause with you in the threat posed by Iran and it is indeed a threat. There is no question about that," Trump told Rivlin.
In Tehran, newly re-elected Iranian President Hassan Rouhani said Iran wants terrorism uprooted in the Middle East and says it is ready for interaction with its neighbors to restore peace in the region.
In his remarks, Rivlin, referring to the prospects of peace in the Middle East, yet fears about Iran, said, "We must be sure we don't go to sleep with a dream and wake up with a nightmare."
At a welcoming ceremony at Ben-Gurion Airport Tel Aviv, Trump said there is now a "rare opportunity to bring security and stability and peace" to the Middle East.
Netanyahu referenced Trump's speech to Muslim leaders in Riyadh on Sunday on the need for a united fight against terrorism. The Israeli leader said his country shares the same commitment to peace and has its hand "extended in peace to all our neighbors, including the Palestinians."
Trump has indicated a desire to restart the Israeli-Palestinian peace negotiations that broke down in 2014.
U.S. Secretary of State Rex Tillerson told reporters traveling with the president that Trump "feels like there is a moment in time here" and an opportunity to advance the process.
"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," Tillerson said.
Trump's schedule Monday included a visit to the Western Wall, an important Jewish holy site, and a visit to the Church of the Holy Sepulchre, the site where tradition says Jesus was crucified and buried in a tomb. On Tuesday, Trump has talks scheduled with Palestinian President Mahmoud Abbas.
WATCH: Visit to Church of Holy Sepulchre
Trump said in March that an Israeli-Palestinian peace deal is "maybe not as difficult as people have thought," though he has not given any indication of how he might approach the issue differently. He has tasked his son-in-law and senior adviser Jared Kushner with leading the effort for the White House.
Trump said during his campaign for president that the best way to negotiate an agreement is taking what he called an "objective" approach to the serious and extremely emotional issues keeping both sides apart. But he has said continued Israeli settlements in the West Bank that Israel seized in the Six-Day War in 1967 do not help the peace process, and has backed off his promise to move the U.S. embassy from Tel Aviv to Jerusalem.
Trump's visit to Saudi Arabia was his first overseas stop as president.
He spoke at a gathering of dozens of Arab and Muslim leaders at a regional summit in Riyadh Sunday, telling them the U.S. wants a coalition of nations "who share the aim of stamping out extremism."