He had met Israeli Prime Minister Benjamin Netanyahu in Jerusalem on Monday.
But Israeli officials were reportedly displeased that Trump tied the future of Israel's relationship with authoritarian Sunni sectarian regimes to progress on making peace with the Palestinians.
"Palestinians are ready to reach for peace", Trump said in his speech at the Israel Museum in Jerusalem, directing his message to Netanyahu and his Cabinet ministers, who, in many occasions, have argued that the Palestinians under Abbas are not a willing partner for peace and that they must undergo changes and meet preconditions before reaching a deal with Israel.
"My reading of the most significance part of his trip, was the way the peace process was approached", he said, explaining Trump has diverted from George W. Bush's 2002 roadmap to peace which brought the worldwide community into the equation. In public remarks in the West Bank town of Bethlehem and in Jerusalem, Trump avoided mention of a two-state solution to the Palestinian conflict, and made no references to controversial Jewish settlements or to recognition of Jerusalem as Israel's capital.
Mr. Abbas reiterated to Mr. Trump "our commitment to cooperate with you in order to make peace and forge a historic peace deal" and to become partners with the USA against terrorism.
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Both players spent the majority of the season in the American Hockey League with the Predators' affiliate in Milwaukee. Jakob Silfverberg leads Anaheim with nine goals, Ryan Getzlaf has 10 assists and Rickard Rakell has 48 shots on goal.
Both world leaders said that they were optimistic that they might be able to work together for peace in Israel and indicated an interested in striking a deal between Israel and Palestine.
"The conflict is not between religions", Mr. Abbas said.
Considered one of the holiest sites in Judaism, the Western Wall is in Jerusalem's Old City, however the U.S. does not recognize Jerusalem as Israel's capital.
But both Netanyahu and Abbas face domestic political challenges. "They are anxious by Trump's language because he did not mention two states", said Ghassan Khatib, a professor of political science at Birzeit University near the West Bank city of Ramallah.
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Other European leaders issued more explicit appeals to the USA government not to abandon global measures against climate change. Li said he believed the two had found a solution on the issue of Chinese quotas for electric cars after a lengthy discussion.
Their votes are off the table if Netanyahu wants to pass a Trump peace deal, and he would thus need to rely on left-of-center legislators - which would cement suspicions in his own party that he's not really one of them.
He became the first sitting USA president to visit the site in east Jerusalem, which Israel occupied in 1967 and later annexed in a move never recognised by the worldwide community.
"It was a great speech because he said the things he had to say and he did not say the things the other presidents usually took advantage of speeches to say", Tzachi Hanegbi, an Israeli minister and ally of Prime Minister Benjamin Netanyahu, told AFP after Trump's closing speech.
Upon arriving in Israel, Trump attempted to hold his wife's hand - but she looked like she wasn't having it.
Trump on Monday landed in Israel, the second stop of his foreign trip. It considers all of Jerusalem its indivisible capital, a status that is not recognized internationally.
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Just back from his nine-day trip to the Middle East and Europe, Trump dismissed recent reports as "fake news". Dubke founded Crossroads Media, a GOP firm that specializes in political advertising.