JUDY WOODRUFF: President Trump is spending tonight in Israel, after a day of talking up peace prospects in the region. It's all part of his first overseas trip since taking office.
We begin our coverage with a report from John Yang.
JOHN YANG: Amid the pomp of President Trump's arrival ceremony in Israel was an issue of policy that's confounded presidents for generations, the Israeli-Palestinian conflict.
PRESIDENT DONALD TRUMP: Now we must work together to build a future where the nations of the region are at peace. We have before us a rare opportunity to bring security and stability and peace to this region.
BENJAMIN NETANYAHU, Prime Minister, Israel: Israel's hand is extended to peace in peace to all our neighbors, including the Palestinians. The peace we seek is a genuine and durable one, in which the Jewish state is recognized, security remains in Israel's hands, and the conflict ends once and for all.
JOHN YANG: The warmth between the two men was evident, as was the Israeli prime minister's pleasure in both the change of U.S. presidents and a new direction on Iran.
BENJAMIN NETANYAHU: I want you to know how much we appreciate the change in American policy on Iran. I want you to know how much we appreciate your bold decision to act against the use of chemical weapons in Syria. And I want to tell you also how much we appreciate the reassertion of American leadership in the Middle East.
JOHN YANG: In an unscripted moment, the president seemed to give the first official confirmation that the highly classified intelligence he gave Russian officials came from the Israelis.
PRESIDENT DONALD TRUMP: I never mentioned the word or the name Israel, never mentioned it during that conversation.
JOHN YANG: In Jerusalem's Old City, Mr. Trump visited two of the holiest sites of Christianity and Judaism: the Church of the Holy Sepulchre, believed by many Christians to be the site of Jesus' tomb, and the Western Wall, believed by Jews to be part of Herod's Second Temple.
Mr. Trump began his trip with a much-anticipated visit to Saudi Arabia. There, he appealed to Sunni Arab leaders to unite to against extremist movements like ISIS and al-Qaida and other militant groups backed by Shiite Iran.
The centerpiece was a speech the White House billed as an address to the Muslim world.
PRESIDENT DONALD TRUMP: A better future is only possible if your nations drive out the terrorists and extremists. Drive them out. Drive them out of your places of worship. Drive them out of your communities. Drive them out of your holy land. And drive them out of this earth.
JOHN YANG: It represented a big shift in tone and temper from the campaign, when he condemned Islam for hating America.
PRESIDENT DONALD TRUMP: This is not a battle between different faiths, different sects or different civilizations. This is a battle between barbaric criminals who seek to obliterate human life and decent people, all in the name of religion, people that want to protect it life and want to protect their religion. This is a battle between good and evil.
JOHN YANG: Mr. Trump also joined the leaders of Egypt and Saudi Arabia to open a center aimed at combating online militant ideology and messaging.
The president's Saudi visit coincided with the reelection of Hassan Rouhani as president of Iran, which was the target of much of Mr. Trump's rhetoric.
Today, Rouhani contrasted the heavy Iranian voter turnout with the lack of elections in Mr. Trump's host kingdom.
PRESIDENT HASSAN ROUHANI, Iran (through interpreter): He has gone to a country where I think the word election has no meaning for them. They have never seen a ballot box. I hope that the day will come that Saudi Arabia will adopt this path.
JOHN YANG: Like the Israelis, the Saudis also welcome the shift in the U.S. approach to Iran that the change in leaders brings, one reason for the opulent Saudi welcome for Mr. Trump, which included a traditional sword dance to underscore the friendship Saudi King Salman extended to the president.
For the PBS NewsHour, I'm John Yang.