Abbas, 82, who was among the negotiators on hand for the historic signing of the Oslo Accords on the White House lawn in 1993, indicated he did feel optimistic that almost a quarter-century later Trump might be the president who finally builds on that initial agreement to forge a final resolution to the conflict.
Throughout his campaign, Trump had promised to move the USA embassy to Jerusalem and supported Israeli settlements in Palestinian territory - concepts that are both held in high regard by staunch pro-Israel groups. "Let's see if we can prove them wrong, okay?"
The US president admired the "continued security coordination" between the PA and Israel, saying he was "actually very impressed and somewhat surprised" that "they get along unbelievably well".
"We need two willing parties", Mr. Trump told Mr. Abbas.
However, Trump did not mention his support for a two-state solution, a longstanding US stance on the issue.
Efforts to overhaul health care, the tax system and government spending have faltered, despite Trump's Republican party controlling not only the White House but both houses of Congress.
Judge Wants More Evidence in Uber Self-Driving Car Dispute
Levandowski repeatedly has invoked his Fifth Amendment rights in the case and declined to comment or produce documents. If the court rules against Uber, it could mean a premature end to the company's autonomous vehicle project.
President Trump promised he might be able to do what eluded his predecessors for decades - brokering peace between the Israelis and the Palestinians.
For his part, Abbas echoed the hope for peace, stipulating peace "based on the vision of the two-state" solution, with Palestine's capital in East Jerusalem.
And we, Mr. President, inshallah, God willing, we are coming into a new opportunity, a new horizon. The deal would not just be about a peaceful, two-state solution, but also about solving the issue of refugees and prisoners "according to worldwide law".
So far, the worldwide community does not recognize Jerusalem as the capital of Israel and not a single foreign country has based their embassies in Jerusalem. Still, Trump chastised Israel in February, asking the Israeli prime minister to "hold back on settlements" being built in the occupied West Bank.
"If Israel and the Palestinians are happy, I'm happy with the one they like the best", he said, standing next to Netanyahu.
The conference marked the first direct meeting between the presidents. He said there could not be lasting peace unless Palestinian leaders spoke in a unified voice against "violence and hate".
Israeli leaders are also waiting for further details from Trump, including whether he will go ahead with his promise to move the U.S. Embassy from Tel Aviv to Jerusalem, a move that would amount to tacit acceptance of Israeli sovereignty over the entire city.
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