Abbas urges armed groups to disband
But Mr Abbas's main rival, Hamas, reiterated it will not disarm and Palestinian officials warned that they will not risk civil war, despite intense international pressure to confront the armed groups.
An ongoing stalemate could hamper the rebuilding of impoverished Gaza and cloud prospects for the resumption of peace talks.
Mr Abbas's security forces have largely displayed weakness since the Israeli withdrawal on Monday. By contrast, Hamas brought tens of thousands into Gaza City's main square on Tuesday - the first day Palestinians controlled Gaza - for the biggest rally by the Islamic militant group ever seen here.
An official celebration set for yesterday on the site of the largest Jewish settlement fizzled out. Mr Abbas had hoped for a large turnout from all factions, but after it became clear that the crowd would be small and most factions would not attend, he cancelled his participation.