Abbas told Trump that his goal is a two-state solution with East Jerusalem as the capital of a Palestinian state, and said the president provides a new opportunity for a peace deal.
"It's a great honor to have President Abbas with us", Trump says according to reports.
During remarks alongside Trump at the White House, Abbas - through a translator - stressed that his people want a Palestinian state with the capital of East Jerusalem and borders along the pre-1967 lines.
"I've always heard that perhaps the toughest deal to make is between the Israelis and the Palestinian", Trump said on Wednesday.
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.
Trump renounced support for a Palestinian state and vowed to move the U.S. embassy to Jerusalem, breaking two tenets of American policy held for decades. "I believe we can be partners - true partners to you - to bring about a historic peace treaty", Abbas said through an interpreter.
During the 2016 campaign, Trump espoused strong pro-Israel views, including a pledge to move the U.S. Embassy in Israel to Jerusalem from Tel Aviv.
"As someone who's worked on this for the last 30 years, I don't think we've ever been at a lower point", he said ahead of the meeting.
Trump said he is "committed to working with Israel and the Palestinians to reach an agreement".
Earlier Tuesday, Vice President Mike Pence held an Israel Independence Day celebration at the Old Executive Office Building, effectively a White House annex.
In a February news conference with Israeli Prime Minister Benjamin Netanyahu, Trump broke with longtime USA policy by raising the one-state idea and withholding clear support for an independent Palestine, though officials quickly stressed he would support any arrangement agreed by the two sides.
The long-shot effort to bring peace - which has eluded U.S. presidents since the 1970s - got off to a rocky start early in Trump's administration. Presidents Barack Obama and George W. Bush held Hanukkah parties at the White House, and Obama celebrated Jewish Heritage Month. He made the trip to Washington while politically unpopular back home, with polls suggesting most Palestinians want him to resign.
Questions have been raised about Trump's choice of his son-in-law, Jared Kushner, who entered the White House with no government experience, to oversee Middle East peace efforts, along with Trump's longtime business lawyer, Jason Greenblatt, as on-the-ground envoy. "Let's see if we can find the solution".
And in his White House meeting with Netanyahu on February 15, Trump raised another sensitive issue: Israeli settlements on land in dispute with the Palestinians.
Trump's top foreign policy advisers were on hand for Abbas' visit.
That could prose major domestic political headaches for Abbas, as he battles unpopularity and challenges from rival factions.