"They ... have taken risks with the blood of Palestinians, with their fate, and dreams and aspirations for an independent Palestinian state," Abbas said.
Abbas is the head of Fatah, which is locked in a power struggle with Hamas in the Palestinian territories.
A delegation from Hamas, which has controlled the Gaza Strip after pushing out security forces loyal to Abbas, is also expected to meet Egyptian mediators in Cairo.
The delegates are expected to seek an extension of the ceasefire between Hamas and Israel.
Speaking from the Syrian capital Damascus, Mohamed Nazzal, an Hamas official, responded that the group whould not rush for talks with Abbas.
"Mahmoud Abbas spoke impulsively, perhaps reflecting the confusion he is living in after the victory of Hamas and the resistance in Gaza," he said.
"We assure him that we are not begging for dialogue and we are not running after it."
Khaled Meshaal, the exiled Hamas political leader, said earlier in the week that the PLO had become obsolete and called for "a new national authority".
His proposal was echoed on Friday by Khalil al-Hayya, a senior Hamas political leader, who said it was "high time the Palestinian people have a new leadership".
Meshaal's comments have not been supported by all Palestinian factions which support Hamas, some of whom argue the PLO should be reformed rather than replaced.
Hamas is not a member of the Palestinian umbrella group which Egypt founded in 1964 and which Fatah took over in 1968.
Ahmed Yousef, an adviser to Ismail Haniya, the head of the Hamas government in Gaza, told Al Jazeera on Sunday that Fatah was the real obstacle to Palestinian unity.
He said Hamas has repeatedly urged Abbas, without success, to reform and restructure the PLO to make it more inclusive.
The war on Gaza - dubbed Operation Cast Lead by the Israelis - ended after the Israeli government declared a unilateral ceasefire.
Hamas declared their own halt to the fighting the following day but there has been no agreement between the two sides.
|Meshaal has criticised the PLO, saying it has become obsolete [File: AFP]
Yousef said that Hamas was waiting for a response from Israel to a proposed formal truce put forward by Egypt.
"We can speak with details about the truce after our delegation examines the Israeli response," he said.
"But for now, things are moving in a positive direction."
Hamas wants an end to the Israeli blockade of the territory, while Israel has demanded an end to Palestinian rocket fire and moves to halt weapons smuggling in the Gaza Strip.
Israel refuses to negotiate directly with Hamas and, as the country approaches parliamentary elections on February 10, cabinet members reiterated that it would not make any direct deals with Hamas.
"A deal with Hamas would give it legitimacy and anyone working towards one with Egypt must understand that," Tzipi Livni, the foreign minister and a candidate for prime minister, told a cabinet meeting.
"I support agreements against Hamas and not with Hamas. We must not hold negotiations on a ceasefire."