The Palestinian president is to meet Trump at the White House for the first time in early April, a Palestinian official said on condition of anonymity.
An Arab League summit is also set for March 29 in Jordan, and Abbas's discussions with Sisi are likely to touch on the meeting.
The meetings come as the American president's administration wades into the decades-old Israeli-Palestinian conflict, with one of his top advisers holding talks with both Abbas and Israeli Prime Minister Benjamin Netanyahu last week.
Egypt and Jordan are the only two Arab countries to have signed peace treaties with Israel, and would be key players in any regional peace process which the Trump administration says it would like to pursue.
Trump cast uncertainty over years of international efforts to foster a two-state solution to the conflict when he met Netanyahu 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.
Media reports have said the tensions involve Cairo's efforts to support one of Abbas's rivals, Mohammed Dahlan, and a failed attempt to hold a regional peace summit including Israel.
Palestinian leaders reportedly opposed such a summit because they did not believe Netanyahu was serious about peace.
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