Trump reiterated his stance that peace can not be imposed by the USA or "any other nation", stressing the parties themselves "must work together to reach an agreement that allows both peoples to live, worship, and thrive, and prosper in peace".
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. "And in that, I also believe that we will be able to resolve the issue of the refugees and the issue of the prisoners", Abbas said.
During the press conference, Trump spoke of wanting to work with Palestinians to fight terrorism, foster private sector development and rule of law, and, of course, to establish a peace deal.
Speaking after the US President finished his statement, Abbas thanked Trump for his invitation and looked forward with working with the White House.
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.
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.
He's taking that as a challenge, and says: "Let's see if we can prove them wrong, OK?"
"It's ... something that I think is frankly maybe not as hard as people have thought over the years", Trump said at the beginning of a lunch with Palestinian President Mahmoud Abbas and senior USA and Palestinian leaders.
"There could be no lasting peace unless the Palestinian leaders speak in a unified voice against incitement to violence and hate".
He has charged son-in-law and senior adviser Jared Kushner with a key role in the effort - just one part of Kushner's sprawling White House portfolio - as well as enlisting former Trump Organization executive Jason Greenblatt, now a special representative for global organizations.
"I believe that we are capable under your leadership and your stewardship and your wisdom as well your great negotiating ability, I believe with the grace of God and with all of your effort, we believe that we can be partners, true partners to you to bring about a historic peace treaty", he said. We believe you're willing.
"Mr. President, it's about time for Israel to end its occupation of our people and of our land".
One of Trump's top advisers, Jason Greenblatt, held wide-ranging talks with both Israelis and Palestinians during a visit in March.
Trump, campaigning for president, pledged to move the embassy to Jerusalem, but has retreated from the promise since assuming office.
Successive presidents have declined to do so despite having congressional authorization under the Jerusalem Embassy Act, warning that the move could endanger US security and potentially upend peace talks between Israel and Palestine.
Abbas said Palestinians are not cultivating a hatred of Israel as he rejected Trump's position, which is also held by Netanyahu. On Tuesday, Vice President Mike Pence said the White House was giving "serious consideration" to the idea.