Their joint appearance came amid Abbas' first visit to the White House under Trump, who, after campaigning on a hardline pro-Israel stance, has in recent weeks softened his tone and suggested that moving closer to a peace deal was a key goal.
Following Trump, Abbas said in remarks translated from Arabic that the Palestinian leadership's "strategic option" is to pursue a two-state solution for the establishment of an independent Palestinian state along the 1967 borders with East Jerusalem as its capital.
"All my life I've heard this is the toughest deal to make", Trump said, and then addressed Abbas and added - "let's prove them wrong".
"It's. something that I think is frankly maybe not as hard as people have thought over the years", he said at the beginning of a lunch with Abbas and senior USA and Palestinian leaders.
"As far as a permanent solution, we believe that this is possible and able to be resolved", Abbas said. "I believe we can be partners - true partners to you - to bring about a historic peace treaty", Abbas said through an interpreter.
The last round of US-brokered peace talks collapsed in 2014.
President Donald Trump meets with Palestinian Authority President Mahmud Abbas in the Oval Office on May 3.
Abbas also said "peace" would allow Israel an opportunity to normalize ties with the Arab states.
"I affirm to you that you are raising our youth, our children, our grandchildren on a culture of peace", Abbas said.
Multiple Sharks Spotted Off San Clemente Coast
A shark advisory remained in effect in parts of southern California Friday following a spike in shark sightings along the coast. Two different schools of great white sharks, like this one, were spotted off beaches in southern California on Wednesday.
Hamas rejects Israel's right to exist, and is regularly at odds with the Palestinian Authority.
Abbas said "it's about time for Israel to end its occupation of our people and our land" - a reference to Jewish settlement building in the West Bank. It said USA and Israeli officials have declined to confirm the trip.
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.
The Palestinian embassy in Doha organised yesterday a stand of solidarity with the Palestinian prisoners in Israeli jails, as the prisoners continue the battle of freedom and dignity (the battle of empty stomachs) by continuing their hunger strike.
And in his White House meeting with Netanyahu on February 15, Trump raised another sensitive issue: Israeli settlements on land in dispute with the Palestinians.
He says "we want to create peace" and he believes "we will get it done".
He praised Trump's "great negotiating ability" and "courageous stewardship" as president as the peace process continued.
"There can not be lasting peace unless the Palestinian leaders speak in a unified voice against incitement to violate - and violence and hate", Trump said. "There can be no lasting peace unless Palestinian leaders speak in a united voice against incitement and hate", he said.