The meeting yesterday comes ahead of Abbas's expected visit to the White House in April and after Trump adviser Jason Greenblatt held wide-ranging talks in Israel and the Palestinian territories earlier this month.
Greenblatt said on Twitter that he held a "very positive meeting" with Abbas ahead of Wednesday's Arab summit in the Jordanian Dead Sea resort of Sweimeh.
"Continued discussion on how to make tangible progress on peace," he said.
Jordan's King Abdullah II is also expected in Washington soon.
Egypt and Jordan are the only two Arab states to have signed peace treaties with Israel and would likely be considered key players in any renewed peace effort.
"All these meetings will have a positive impact on the Palestinian issue," Abbas said.
An Arab peace initiative dating back to 2002 has offered normalised relations with Israel in exchange for resolving the decades-old Israeli-Palestinian conflict.
Trump has said he would be interested in pursuing some form of regional peace initiative.
Trump has sent mixed signals over how he will address the Israeli-Palestinian conflict.
He cast uncertainty over years of international efforts to foster a two-state solution to the conflict when he met Israeli Prime Minister Benjamin Netanyahu at the White House last month.
At that meeting, Trump broke with decades of US policy by saying he was not bound to a two-state solution to the conflict and would be open to one state if it meant peace.
UN Middle East envoy Nickolay Mladenov said last week that Israel has ignored a Security Council resolution approved in December demanding a halt to settlement activity in occupied Palestinian territory.
An opinion poll released by a right-wing Israeli think tank on Wednesday found that Jewish Israelis' willingness to agree to a withdrawal from the West Bank as part of a peace agreement had fallen from 60 per cent in 2005 to 36 per cent in 2017.
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