"We regret shedding Palestinian blood by Palestinian hands in clashes that crossed all the red lines."
Monday's four-way summit in the Red Sea resort of Sharm el-Sheikh will be attended by King Abdullah of Jordan, Ehud Olmert, prime minister of Israel, and Abbas.
Cairo has already moved its move its representative from Gaza to Ramallah in the West Bank, where the rival Fatah movement has largely retained control.
Meanwhile, heads continue to roll in the Fatah top brass. On Saturday, Abbas dismissed Suleiman Khader, the former commander of his security forces in the central Gaza Strip.
Khader handed the headquarters of the Abbas-allied forces there to Hamas without a fight, and a statement was released by Abbas' office saying he had acted in a cowardly manner.
The dismissal follows the resignation of Rashid Abu Shbak, Abbas' top security commander, on Friday.
Abbas also announced he has appointed a panel to examine the failure of his security forces to prevent the violent takeover of the Gaza Strip by Hamas.
An announcement from Abbas' office said the committee would be headed by Zakariya al-Agha, a Fatah leader in Gaza, and will co-ordinate with a similar panel set up in the West Bank last week.
For its part, Hamas has accused Fatah and Israel of a "dual conspiracy" against the group in the West Bank after the arrest of Saleh al-Aruri, who officials said founded Hamas' Qassam Brigades armed wing in the area.
Al-Aruri was captured by Israeli forces in a village north of Ramallah. Israel released him from custody in March 2007 after he spent 15 years in an Israeli prison for founding the Qassam Brigades, an Israeli security source said.
The source said al-Aruri was arrested again on Saturday after he "continued to openly operate as part of the Hamas terror organisation".
Israel looks set to is continue its attempts to isolate Hamas economically, diplomatically and militarily in the Gaza Strip by beginning to transfer funds to the emergency government set up by Abbas and easing some travel restrictions in the West Bank, officials said on Saturday.
The money is part of an initial package of "gestures" that Olmert will present to his cabinet for approval on Sunday before talks with Abbas on Monday at Sharm el-Sheikh.
Officials said the gestures could be expanded in the future to include giving Abbas' security forces control over additional areas of the occupied West Bank.