"The method used by Hamas is atrocious and inhumane. I do not know this small group but I think it is an offshoot of Hamas," said Abbas while chairing the weekly meeting of the Palestinian government in Ramallah.
Hamas, which has controlled the Gaza Strip since June 2007, crushed on Friday night a small group called Jund Ansar Allah that challenged its authority. The clashes in the southern Gaza Strip town of Rafah left 24 people dead.
At the cabinet meeting, Palestinian Prime Minister Salam Fayyad presented his government's plan for the establishment of a Palestinian state "within the next two years."
Negotiations with Israel for the creation of such a state have been frozen since December 2008, and the Palestinian Authority calls for the cessation of Jewish settlements in the territories, a demand which has been rejected by Israeli Prime Minister Benjamin Netanyahu's right-wing government.
Abbas said during the cabinet meeting that negotiation was the only path to statehood, espousing non-violence after his Fatah party backed an option of "resistance" against Israeli occupation.
"We are peace seekers," the Western-backed leader said. "The main and the only path is the path of peace and negotiations. We don't have any other path and we do not wish to use any other path."
Hamas security forces in Gaza (Photo: AP)
It was the cabinet's first meeting since the dominant Fatah movement which Abbas heads held a congress this month, at which he reasserted the Palestinian option of "resistance" against Israel's occupation of the West Bank.
He did not define resistance but gave examples of civil disobedience. He said terrorism was counter-productive.
But the language, adopted in a policy document, drew criticism from Israel, which pursued peace negotiations with Abbas until talks stalled nearly a year ago and which expects him to resume talks in the near future.
Analysts said Abbas was engaged in a political balancing act with the West, Israel and factions of his own movement.
"Abbas was seeking to reduce American and Israeli anger after the congress," said political analyst Hani Masri.
"He wants to reiterate that nothing has changed after the congress. He is adopting the same path."
Analyst Basem Zubeidi of Bir Zeit university said Abbas "spoke about resistance at the congress in order to satisfy all factions, and in order to regain legitimacy.
"Abbas wants to assure everyone and I think he has succeeded in doing that and he has succeeded in showing that his way is the way of negotiations."
Fatah's congress in Bethlehem was its first in 20 years and first without the late Yasser Arafat to dominate proceedings. Palestinian commentators said Abbas was strengthened by the election to its executive body of men from a younger generation.
But Abbas may face problems in Fatah's Central Committee in the future if he is seen to dismiss the option of "resistance" out of hand, the analysts said.
Some Arab commentators have criticized the Fatah congress for blunting the Palestinian independence movement.
"Without exaggeration it is possible to say that one of the first results of the Fatah conference was political confusion," wrote Al-Jazeera television's commentator Mo'men Basisoand.
He said Fatah "has become completely hostage to the international political position, which complements the Israeli position. This is another way of explaining Abbas' insistence on following the negotiation line."
In his statement on Monday, Abbas said Israel must stop West Bank settlement activity in all its forms, and if it does so, peace talks will resume.
Netanyahu has resisted a settlement freeze, as dictated by the US-backed 2003 Road Map.
"We want to start from the point where the negotiations left off," said Abbas, indicating there would be no retreat from positions already negotiated with the former Israeli government of Ehud Olmert.
Reuters and AFP contributed to this report