"The President's ultimate goal is to establish peace in the region," said White House press secretary Sean Spicer.
That long-shot effort -- which has eluded US presidents since the 1970s -- got off to a rocky start early in Trump's adminstration.
Trump renounced US support for a Palestinian state and vowed to move the US embassy to Jerusalem, breaking two tenets of US policy held for decades.
Vice President Mike Pence on Tuesday said Trump is still "giving serious consideration into moving the American embassy in Tel Aviv to Jerusalem."
That move would likely spark Palestinian fury and is privately seen by many in the Israel and US security establishments as needlessly inflammatory.
At the same time, Trump has urged Israel to hold back on settlement building in the West Bank, a longstanding concern of Palestinians and much of the world.
Pence said Trump is "personally committed to resolving the Israeli and Palestinian conflict" and "valuable progress" is being made.
"Momentum is building and goodwill is growing," he said at an Israeli independence day event at the White House.
Abbas makes the trip to Washington while politically unpopular back home, with polls suggesting most Palestinians want the 82-year-old to resign.
Abbas's term was meant to expire in 2009, but he has remained in office with no elections held.
But he will be hoping Trump can pressure Israel into concessions he believes are necessary to salvage a two-state solution to one of the world's longest-running conflicts.
Palestinian officials have seen their cause overshadowed by worry over global concerns such as the war in Syria and Islamic State group jihadists, and want Trump's White House to bring it back to the forefront.
The meeting Wednesday is a sign that "Trump's approach to the Israeli-Palestinian conflict is more conventional than anyone expected," said Ilan Goldenberg of the Center for New American Security.
"The big question now is what Trump will try to accomplish during this first meeting. If he goes for the home run and tries to restart negotiations, he is likely to fail."
"Instead, Trump and his team should focus on incremental steps to improve the situation on the ground, preserve the possibility of the two-state solution at another time, and set conditions for negotiations in the future."
One of Trump's top advisers, Jason Greenblatt, held wide-ranging talks with both Israelis and Palestinians during a visit in March.
Abbas and Trump spoke by phone on March 11, and there are suggestions the US president could visit the Middle East this month.
A group of three influential Republican Senators -- Marco Rubio, Tom Cotton and Lindsey Graham -- have called on Trump to ask Abbas to stop funding Palestinian prisoners and their families.
That could prose major domestic political headaches for Abbas, as he battles unpopularity and challenges from rival factions.
But according to former White House official Dennis Ross, Trump is in some ways helping Abbas by extending the White House invite.
"The president, in some ways, has already added to his relevancy by inviting him to come."
But mutual distrust between Palestinians and Israelis will be a formidable, if not impossible, barrier for Trump to overcome.
"The gap between the parties has probably never been greater, both psychologically and practically," said Ross.
"In my mind, as someone who's worked on this for the last 30 years, I don't think we've ever been at a lower point."