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.
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.