"It's something that I think is frankly, maybe not as hard as people have thought".
This was the first face-to-face meeting with a U.S. president for Mr Abbas, who has low popularity ratings in Palestine at the moment. "I would love to be a mediator, an arbitrator or a facilitator, and we will get this done".
The long-shot effort to bring peace - which has eluded United States presidents since the 1970s - got off to a rocky start early in Trump's administration.
Several U.S. presidents before Trump have come into office expressing confidence that they were the ones who would finally bring peace to the region. The Palestinian leader said a peace agreement could be reached under "the courageous leadership of Donald Trump". "We want to create peace between Israel and the Palestinians".
H.R. McMaster said the president's novel style coupled with the threat posed by the Islamic State and Iran could bring about Israeli-Arab peace.
"Mr. President, it's about time for Israel to end its occupation of our people and of our land", Abbas said. He said he had "hope" about prospects for peace with Trump in that role as he praised the President for his negotiating acumen.
In February, Trump met with Israeli Prime Minister Benjamin Netanyahu and broke with decades of USA policy by signaling he might be open to a one-state solution.
Trump's promise to move the U.S. Embassy to Jerusalem from Tel Aviv, strongly opposed by Palestinians, has been shifted to the back burner, and he has asked Netanyahu to put unspecified limits on settlement activity. "Now, Mr. President, with you we have hope". For Abbas and the Palestinians, there is only one solution.
President Trumppromised Wednesday to make peace in the Middle East a top priority, vowing to do "whatever is necessary" to reach a historic deal between Israel and the Palestinians.
Only a two-state solution, Abbas said, would allow Palestinians to focus on fighting terrorism and enable Arab states to establish normal relations with Israel.
Standing beside Trump, Abbas later told reporters that the strategic choice to solve the Israeli-Palestinian conflict was "to bring about peace based on the vision of the two state".
He told Mr Abbas: "We will get it done".
With the global focus on Syria's bloody civil war and the threat posed by Islamic State, Palestinian officials have been keen to raise their cause up the White House agenda. "And it will be to the credit of the civilized world and the American administration to stop the darkness that we have been suffering from for many years". Abbas's explicit citation of the two-state solution also suggests a nuanced difference with Trump, who has retreated from 15 years of USA policy favoring the two-state outcome.