Egyptian officials also demanded that the protesters stay at least 500 meters away from the border.
Abbas is reportedly threatening cessation of all funds to the Strip if Hamas refuses.
Fatah officials head to Cairo for truce, unity talks.
"Our weapons will remain in our hands and there are no conditions regarding Hamas's right to [continue] the resistance."
Hamas, Israel differ on whether ‘calm-for-calm’ deal reached in South
Hamas leader Ismail Haniyeh said the senior officials of his movement held intensive discussions with representatives of all Palestinian factions in the Gaza Strip about the cease-fire proposal.
No operative decisions were made public, and a statement afterward said only that the IDF is ready for anything.
Abbas was apparently referring to previous recommendations by the Central Council and the Palestine National Council, the PLO’s parliament, to sever ties with Israel.
Egypt has exerted heavy pressure on Hamas and Fatah to end the enmity between them.