By Agence France-Presse
The US president greeted Abbas on the White House lawn, barely two and a half months after having received Israeli Prime Minister Benjamin Netanyahu.
"Hopefully something terrific can come out between the Palestinians and Israel," the Republican president said as their meeting got underway in the Oval Office.
Abbas sat smiling at Trump's side, but made no remarks.
The two leaders were to deliver a joint statement after their talks, although no press conference was planned.