At a White House meeting with Palestinian leader Mahmoud Abbas, Trump pledged to reinvigorate the stalled Mideast peace process that has bedeviled his predecessors and said he would serve as "a mediator, an arbitrator or a facilitator" between the two sides.
Trump further said that that the two sides must continue to build their partnership to counter and defeat terrorism.
Trump affirmed that he hopes to "start a process" for peace negotiations and said that he had spoken with Israeli Prime Minister Benjamin Netanyahu about jump starting peace talks.
"I affirm to you that we are raising our youth, our children, our grandchildren on a culture of peace", Abbas said, notwithstanding the anti-Israel hate and incitement to violence prevalent in Palestinian schools, media and cultural events.
The meeting Wednesday is a sign that "Trump's approach to the Israeli-Palestinian conflict is more conventional than anyone expected", said Ilan Goldenberg of the Center for New American Security.
Abbas spoke in a meeting with Arab ambassadors late Thursday before leaving Washington where he had met with President Donald Trump earlier in the week about resuming peace talks with Israel.
Palestinian officials had earlier announced that they may accept a USA regional solution to the conflict with Israel, but it should be based on the 2002 Arab Peace Initiative, which demands a Palestinian state on the 1967 borders and the return of refugees in exchange for full Arab normalization with Israel.
"I've always heard that perhaps the toughest deal to make is between the Israelis and the Palestinians", Trump said on Wednesday.
The trip would be Mr Trump's first outside the United States as president. Reaffirming his commitment to a two-state solution, he called on Israel to recognize Palestinian statehood just as Palestinians recognize the state of Israel.
Abbas, whose electoral mandate expired in January 2009 but has been extended by decree ever since, said it was time for Israel "to end its occupation of our people and of our land", declaring that the Palestinians are "the only remaining people in the world that still live under occupation". United States and Israeli officials have declined to confirm the visit.
Trump's administration is widely perceived as staunchly pro-Israel and the acknowledgment of the Palestinians was welcomed by Ghassan Khatib, a professor of political science at Birzeit University in the West Bank.
Hussein al-Sheikh, head of the Civil Affairs Department in the West Bank, said Abbas' government would stop paying for the electricity Israel sends to Gaza, worth at least $11 million a month.
Trump has faced deep scepticism at home and overseas over the chances for him to achieve any quick breakthrough, not least because his administration has yet to articulate a cohesive strategy for restarting the moribund peace process.
Despite his pro-Israeli campaign trail rhetoric, since entering the White House Mr Trump has caught some Israeli hard-liners off guard with the suggestion the Netanyahu coalition government should "hold back" on settlement building, and his administration has equivocated over whether the U.S. embassy will move from Tel Aviv to Jerusalem as promised.