The US president greeted Abbas on the White House lawn, barely two and a half months after having received Israeli Prime Minister Benjamin Netanyahu.
"I've always heard that perhaps the toughest deal to make is the deal between the Palestinians and the Israelis", Trump said.
Abbas pointed toward a likely partnership while crediting Trump's "great negotiating ability".
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. Reaffirming his commitment to a two-state solution, he called on Israel to recognise Palestinian statehood just as Palestinians recognise the state of Israel.
President Donald Trump expressed confidence Wednesday that his administration can help the Israelis and the Palestinians find peace, a goal that has vexed USA efforts for decades.
Trump and Abbas also discussed ways to enhance security cooperation to assist the Palestinians in countering terrorism, as well as stimulating the Palestinian economy.
Abbas told Trump: "I look much forward to working with you in order to come to that historical agreement, historic deal to bring about peace".
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On Tuesday, the official said that the Pentagon had been instructed to determine its force levels in Afghanistan. Even backers of a more robust approach concede that the chances of a major peace deal to end the war are low.
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The US president promised to do "whatever is necessary" to facilitate an agreement between the Palestinians and Israelis, who "must work together to reach an agreement that allows both peoples to live, worship and thrive and prosper in peace".
During lunch with Abbas, Trump raised concerns about Palestinian payments to terrorists and their family members.
Trump did directly implore the Palestinian leadership to end what Israel and the United States say is anti-Israel rhetoric.
"There can be no lasting peace unless the Palestinian leaders speak in a unified voice against incitement to violence and hate", Trump said, standing next to Abbas.
The Palestinian leader expressed his support for a two-state solution to the conflict - which is not supported by the majority of Palestinians - as well as the longheld Palestinian desire for a capital in East Jerusalem.
Trump sent his Middle East envoy, Jason Greenblatt, to Jerusalem and Ramallah in March to explore possible roles for the U.S.in the peace process. It was part of the vigorous dose of optimism on display as Trump and Abbas showered each other with praise.
He also at the time asked Netanyahu to stop building settlements in the West Bank, also known by its ancient names of Judea and Samaria, and Gaza Strip for a short time. But in a February news conference with Israeli Prime Minister Benjamin Netanyahu, Trump broke with longtime USA policy by raising the idea of a one-state peace agreement, withholding clear support for an independent Palestine.