"We will get this done," Trump vowed.
Trump reiterated the need for Israelis and Palestinians to broker a peace through direct negotiations and called on Palestinian leaders to "speak in a unified voice against incitement to violence and hate."
"There's such hatred, but hopefully there won't be such hatred for very long," Trump said, speaking alongside Abbas in the Roosevelt Room.
The Palestinian leader expressed his support for a two-state solution to the conflict and the long-held Palestinian desire for a capital in East Jerusalem, welcoming Trump's role as a mediator in peace negotiations. He said he had "hope" about prospects for peace with Trump in that role as he praised the President for his negotiating acumen.
"I believe that we are capable under your leadership and under your courageous stewardship and your wisdom as well as your great negotiating ability ... I believe we can be partners -- true partners to you -- to bring about a historic peace treaty," Abbas said through an interpreter. "Now, Mr. President, with you we have hope."
Trump expressed his desire to have Palestinians and Israelis draw on the Oslo Accords that Abbas signed onto as the Palestinian negotiator in 1993 and said he hoped the Palestinian leader would soon sign "the final and most important peace agreement."
But while Trump spoke broadly about his desires for a peace deal and some of the barriers to a deal, Abbas drilled down on the specific complaints and demands of Palestinians.
Abbas spoke of the importance of providing solutions that would address the situation Palestinian refugees and those imprisoned in Israeli prisons, referring to "the suffering of my people."
"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.
Trump on Wednesday did not address Israeli settlements in the West Bank, which he has asked the Israeli Prime Minister to halt, nor did he address the terrorist group Hamas, which controls Gaza and earlier this week opened the door to at least a temporary deal for a Palestinian state based on the 1967 borders.
Abbas' visit comes more than two months after Israeli Prime Minister Benjamin Netanyahu visited Trump at the White House, where the two men's chummy relationship was on full display.
But while Trump's meeting with Netanyahu signaled an era of warmer US-Israel relations than had existed under President Barack Obama, Trump also slightly moderated his stance on the Israeli-Palestinian conflict from the unequivocal support he promised Israel during the campaign.
Trump urged Netanyahu to "hold back on settlements for a little bit," and while he said he'd "love" to see the US embassy move to Jerusalem, he offered no indication it would happen soon.
Vice President Mike Pence on Tuesaday said Trump is giving "serious consideration" to moving the US Embassy from Tel Aviv to Jerusalem, which he pledged to do during the presidential campaign, but did not offer a timeline for that move.
Trump must decide by June 1 whether to sign a six-month waiver forestalling a move. Every US president has signed such a waiver twice a year after a law was passed in 1995 mandating the relocation of the embassy unless the White House certifies doing so would raise national security concerns.
Trump ignored a question shouted by a reporter during his Oval Office meeting about whether he still plans to move the US Embassy.
Trump's top foreign policy advisers were on hand for Abbas' visit. Vice President Mike Pence, National Security Adviser H.R. McMaster and Secretary of State Rex Tillerson were all slated to join the talks alongside the US special representative for international negotiations, Jason Greenblatt. Trump son-in-law and senior adviser Jared Kushner, who has spearheaded much of the administration's efforts to tackle the Israeli-Palestinian conflict, also joined in on the meeting, as well as White House chief of staff Reince Priebus and chief strategist Steve Bannon, US officials said.
Trump was expected to raise the issue of the Palestinian Authority's compensation of Palestinians whose family members are killed while carrying out a terrorist attack against Israelis.
The payments, established in the 1990s by the Palestine Liberation Organization (PLO) and continued by the Palestinian Authority, have prompted calls from members of Congress to cut off funding to the Palestinians.