Israel and the Palestinians have not held direct talks for more than three years and Trump acknowledged it was "one of the toughest deals of all".
"Making peace, however, will not be easy".
Trump made the remark alongside Israeli Prime Minister Benjamin Netanyahu in a speech at the Israel Museum.
"President Abbas noted that he was ready to begin negotiating (with Israel) immediately", the readout said. The legacy of the Arab Spring and the lingering dissent against authoritarian rule inside most Arab states could mean that Trump's overtures could backfire soon.
"President Abbas assures me he is ready to work towards that goal in good faith, and Prime Minister Netanyahu has promised the same", Mr. Trump said.
"He didn't reprimand Israel for settlements, he didn't commit the United States to a two-state vision".
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Despite enjoying greater possession, Bosz's inexperienced team struggled in what was the club's first European final since 1996. Unfortunately, rival supporters saw it as a very different kind of treble as they took to social media after the game.
"The time has come to prove to the Israelis, the Palestinians and the entire world that an important segment of the Israeli population is opposed to occupation and wants a two-state solution", he added.
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"It was a visit of intent, of his intent to reach out and help us reach a final agreement".
Trump heads next to Europe, where planned meetings with world leaders on the economy and trade could be overtaken with discussion of terrorism and security. What was clear is that Trump is seeking a new relationship between Israel and its traditionally hostile Middle Eastern neighbours.
He was accompanied by the Rabbi of the Western Wall, Shmuel Rabinowitz, who said on Israel Radio that he recited two psalms with the USA leader.
"The real question is if there is something substantive happening behind closed doors". He has already visited Saudi Arabia and Israel.
Mr Abbas had sought to convince the unpredictable US President to remain committed to an independent Palestinian state.
Abbas has previously demanded a freeze on settlement construction before returning to the negotiating table. "And that's always been a problem", he said.
While Tillerson did not fully explain his comments, the mere suggestion that solving the Israeli-Palestinian is key to solving the broader problems of the Middle East in challenging violent extremism is "nonsensical", said Tamara Cofman Wittes, a Senior Fellow in the Center for Middle East policy at Brookings Institute.