"So, we are telling you right now, that Iran will not have nuclear weapons", he said.
The speech at the Museum was Trump's last stop in Israel, before flying to Rome to meet with Pope Francis.
They were joined by Israeli prime minister Benjamin Netanyahu and his wife Sara, as well as daughter Ivanka Trump and son-in-law Jared Kushner, who are White House senior advisers. "But with determination, compromise, and the belief that peace is possible, Israelis and Palestinians can make a deal".
The two leaders also agreed on the need to counter Iran and its proxies, including by building strong military capabilities to protect Israel and the region from Iranian aggression.
Trump, in Bethlehem, vowed to do "everything I can" to bring peace to the Middle East, echoing sentiments of several of his predecessors who tried and failed to achieve the same goal.
Their talks came with hundreds of Palestinians in Israeli jails on hunger strike since April 17, which Abbas referred to in his remarks after meeting Trump.
There was no official criticism of Israel's occupation and other violations of worldwide law and numerous United Nations resolutions.
What may be surprising and make Trumps visit appear less lopsided - some would say surprising, is that he went to the wall alone, without Israeli leaders. I will call them losers from now on.More news: Park Geun-hye: South Korea's impeached president goes on trial for corruption
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"They're all saying I did, so you have another story wrong". The Palestinians want a state in the West Bank, Gaza Strip and east Jerusalem, captured by Israel a half century ago. "If it does, I would say to you that it goes further in my mind as a member of the intelligence committee than just the focus on the Russian Federation investigation". "Believe me", said Mr. Trump to a round of loud cheers and applauds in support. Well - I hope this heralds a real change, because if the attacker had been Palestinian and the victims had been Israeli children, the suicide bomber's family would have received a stipend from the Palestinian Authority.
Ahead of the trip, a Trump official got in a heated argument with Israelis after claiming the Kotel was "part of the West Bank".
That stands in sharp contrast to Barack Obama, who focused heavily on the Arabs' desired (initial) outcome of the peace process.
He has taken a softer position on the contentious issue of Israeli settlements, suggesting that their expansion rather than their presence might hamper the search for peace.
The status of Jerusalem is ultra-sensitive and has been among the most hard issues in Israeli-Palestinian peace talks, stalled since April 2014.
During his election campaign, Trump also advocated breaking with decades of precedent and moving the American embassy from Tel Aviv to Jerusalem, alarming Palestinians.
This is published unedited from the PTI feed.