Mr Trump said he had always heard "this was the toughest deal to make, let’s prove them wrong.”
This was the first face-to-face meeting with a US president for Mr Abbas, who has low popularity ratings in Palestine at the moment.
Mr Trump said that Mr Abbas was present for the first peace agreement signed between Israel and Palestine and wants to be the US president that has Mr Abbas “sign the last agreement” between the two parties.
He noted that no “agreement can be imposed by the US or any other nation” but said he would “love to be a mediator, arbitrator, or facilitator” for the peace process.
Mr Trump has tasked his son-in-law Jared Kushner to help though the former real estate professional has no discernable foreign policy experience.
The meeting is expected to be “tense,” as the Los Angeles Times described it.
Donald Trump's first 100 days: in cartoons
Donald Trump's first 100 days: in cartoons
Donald Trump's first 100 days in office were marred by a string of scandals, many of which caught the eye of the Independent's cartoonists
Trump's first 100 days have seen him aggressively ramp up tensions with his nuclear rivals in North Korea
Mr Trump has warned of a "major, major conflict" with the pariah nation lead by Kim Jong Un
Mr Trump dropped the "mother of all bombs" on alleged ISIS-linked militants in Afghanistan, amid an escalation of US military intervention around the globe
Mr Trump has been accused of falling short of the standards set by his predecessors in the Oval Office, including Franklin D Roosevelt
The tycoon's ascension to the White House came at a time when the balance of power is shifting away from Western nations like those in the G7 group
Western politicians, including the British Conservative party, have been accused of falling in line behind Mr Trump's proposals
Brexit is seen to have weakened Britain, reducing still further any political will to resist American leadership
Mr Trump's leadership has been marked by sudden and unexpected shifts in global policy
Trump's controversial missile strike on Syria, which killed several citizens, was seen by some analysts as an attempt to distract from his policy elsewhere
The President has also spent a large majority of his weekends golfing, rather than attending to matters of state
Though free of gaffes, a visit from Chinese president Xi Jinping spotlighted trade tensions between the two states
One major and unexpected setback came when Mr Trump's Healthcare Bill was struck down by members of his own party
Mr Trump has been a figure of fun in the media, with his approval at record lows
A string of revelations about Mr Trump's financial indiscretions did not mar his surge to the White House
Outgoing President Barack Obama was accused of wiretapping Trump Tower by his successor in America's highest office
The alleged involvement of Russian intelligence operatives in securing Mr Trump the presidency prompted harsh criticism
The explosive resignation of Security Adviser Michael Flynn, who lied about his links to the Russian ambassador, was just one scandal to hit the President
Many scandals, such as the accusation Barack Obama was implicated in phone-hacking, first broke on Mr Trump's Twitter feed
Donald Trump's election provoked mass protests in the UK, with millions signing a petition to ban him from the country
Donald Trump cited a non-existent terror attack in Sweden during a campaign rally
Donald Trump stands accused of stoking regional tensions in Eastern Asia
North Korea has launched a number of failed nuclear tests since Mr Trump took power
Theresa May formally rejected the petition calling for Mr Trump to be banned from the UK
When Mr Trump's initial so-called Muslim ban was struck down by a federal justice, the President mocked the 69-year-old as a "ridiculous", "so-called judge"
A week after his inauguration, Theresa May met with Mr Trump at the White House
Donald Trump's first days in office were marked by a hasty attempt to follow through on many of his campaign promises, including the so-called Muslim ban
Donald Trump's decision to ban citizens of many majority-Muslim countries from the US sparked mass protests
Revelations about Donald Trump's sexual improprieties were not enough to keep him from being elected President
British PM Theresa May was criticised by many in the press for cosying up to the new President
One of Mr Trump's top aides, Kelly Anne Conway, was mocked for describing mistruths as "alternative facts"
British PM Theresa May was quick to demonstrate that her political aims did not hugely differ from Mr Trump's
Donald Trump's inauguration, on 20 January 2017, sparked protests both at home and abroad
Mr Abbas allegedly played a role in pushing the vote through and members of Mr Trump’s team have not forgotten it, according to the LA Times.
Despite that, Mr Abbas was almost effusive in his faith in Mr Trump, saying that the Palestinian people are “capable, under your stewardship...and great negotiating ability” to be true partners with the US.
He was also clear that Palestine wants a two-state solution, a long-held US stance that Mr Trump was open to changing earlier this year. US Ambassador to the UN Nikki Haley, and other officials clarified that the US is committed to a two-state solution.
The Palestinian leader said he hoped to “resolve the problem of refugees and prisoners” with regards to international law in whatever agreement may be signed.
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.
Mr Trump also said the two leaders would discuss economic opportunities for the people of Palestine through private sector development in the region, but that no lasting peace would be achieved “unless Palestinian leaders speak in a unified voice.”
The two also spoke of defeating terror group Isis and general counter-terrorism efforts in the region.Reuse content