Trump, appearing with Abbas at the White House, told reporters about the peace deal, "We will get this done".
US officials had said ahead of Wednesday's meeting that Trump would press Abbas to end payments to families of Palestinians imprisoned in Israeli jails.
At an event in the Roosevelt Room, Trump said he was calling on Congress to work with the administration to extend school choice "to millions more children all across the United States of America", including low-income Hispanic and African-American children.
Abbas said he hoped the United States could be "true partners" to bring about a historic settlement.
Even so, he also acknowledged getting both sides to agree on a peace plan could be an uphill climb, calling Middle East peace the "toughest deal to make".
Lerman said in a conference call hosted by The Israel Project, which publishes The Tower, that Trump's approach to the peace process would mark a return to the stance adopted by former Secretary of State James Baker, who said, "we can not want peace more than the sides themselves".
President Donald Trump meets with Palestinian Authority President Mahmud Abbas in the Oval Office on May 3. "But we will be working diligently, and I think there's a very, very good chance, and I think you feel the same way". "There is no reason there's not peace between Israel and the Palestinians - none whatsoever".
"Mr. President, it's about time for Israel to end its occupation of our people and of our land", Abbas said, referring to the Palestinian territories in the West Bank under Israeli control.
"We will get it done".
Trump renounced support for a Palestinian state and vowed to move the USA embassy to Jerusalem, breaking two tenets of American policy held for decades.
One of Mr Trump's requests during the private meeting will likely be that Palestine stops paying the families of those who carry out terrorist attacks against Israel.
Trump, they added, will reiterate his belief that Israeli settlement construction on land claimed by the Palestinians does not advance peace prospects.
"It was on these grounds that President Abbas stood with a courageous peacemaker, then-Israeli Prime Minister Yitzhak Rabin".
Trump urged Netanyahu to "hold back on settlements for a little bit", and while he said he'd "love" to see the USA embassy move to Jerusalem, he offered no indication it would happen soon. "Let's see if we can prove them wrong, okay?"
President Donald Trump is expressing optimism for resumed peace talks between the Palestinians and Israel.
He quickly reasserted the goal of the creation of a Palestinian state as vital to any rejuvenated peace process.
Trump told Abbas he wants his signature on the final peace agreement.
Trump, however, didn't mention any specific parameters of such a deal, other than saying that it would involve two states.