HARI SREENIVASAN: The president continued his lengthy overseas trip today, ending his stay in Israel and a visit to the West Bank. It was the end of four days in the Middle East, after a packed schedule that included summits, elaborate dinners, and high-stakes meetings.
John Yang reports.
JOHN YANG: President Trump crossed the imposing security wall separating Israel and the West Bank to meet with Palestinian leader Mahmoud Abbas in Bethlehem, part of Mr. Trump's quest to jump-start long-dormant Israeli-Palestinian peace talks.
PRESIDENT DONALD TRUMP: I intend to do everything I can to help them achieve that goal. President Abbas assures me he is ready to work toward that goal in good faith, and Prime Minister Netanyahu has promised the same.
JOHN YANG: Abbas outlined what's called the two-state solution, a Palestinian homeland on the territory that Israel seized 50 years ago in the Six-Day War.
PRESIDENT MAHMOUD ABBAS, Palestinian Authority (through interpreter): Our fundamental problem is with the occupation and settlements, and failure of Israel to recognize the state of Palestine, in the same way we recognize it. It undermines the realization of a two-state solution. The problem is not between us and Judaism. It's between us and occupation.
JOHN YANG: Later, speaking in Jerusalem, Mr. Trump acknowledged there would be hurdles.
PRESIDENT DONALD TRUMP: Both sides will face tough decisions. But with determination, compromise and the belief that peace is possible, Israelis and Palestinians can make a deal.
JOHN YANG: Missing from Mr. Trump's comments? An explicit endorsement of a two-state solution, which has been U.S. policy for more than a quarter-century.
Daniel Estrin is Jerusalem correspondent for NPR News.
DANIEL ESTRIN, NPR: He spoke a lot about peace, but he was very short on specifics. And that was very emblematic of his whole trip here. He didn't want to wade into any thorny issues.
He didn't talk about a two-state solution. He didn't talk about Israeli assessments in the West Bank, where Palestinians want to build a Palestinian state. He didn't talk about the U.S. Embassy. This trip was much more about smiles. It was much more about relationship-building.
JOHN YANG: Do you see much reason for optimism that President Trump is going to get these talks, this peace process going again?
DANIEL ESTRIN: Clinton tried. Bush tried. Obama tried. They all failed at bringing peace. And so many people I spoke to here, Israelis and Palestinians, said, why should Trump be any different?
I even met a Palestinian woman yesterday who said she read Trump's book "How to Get Rich." She admired Trump's business success, but she said, that doesn't translate into making someone a peacemaker.
So, while there is that cynicism, there are also people on both sides who think that actually Trump perhaps might be the one to seal the deal.
JOHN YANG: On the last day of his Israel stop, Mr. Trump visited Yad Vashem, the nation's Holocaust memorial.
PRESIDENT DONALD TRUMP: Words can never describe the bottomless depths of that evil or the scope of the anguish and destruction. It was history's darkest hour.
JOHN YANG: He signed the guest book: "It is a great honor to be here with all of my friends. So amazing, and will never forget."
Mr. Trump's whirlwind tour of one of the Middle East's most intractable problems ended with a departure ceremony.
Tonight, the president is in Rome, where, tomorrow, he is to meet Pope Francis.
For the PBS NewsHour, I'm John Yang.