Abbas, whose Fatah movement has been at loggerheads with Hamas, said maintaining the truce could have helped the Palestinians avoid the raids, which have so far killed more than 280 people over the past two days.
Nour Odeh, Al Jazeera's correspondent in Ramallah, reported that senior figures had supported Abbas in his call on Hamas not to abandon the truce.
She added that during an Israeli election year, a hardline position towards Palestinians has always won more seats, making the timing particularly risky for Hamas.
"Not just Abbas, but people close to the circles of decision-making in key Arab states, said that Hamas was warned that breaking the ceasefire or not keeping it would result in mayhem and bloodshed," she reported.
Ayman Mohyeldin, Al Jazeera's correspondent in Gaza, said the stance at all levels of the Hamas leadership was the same: "They will remain defiant in the face of any attacks and that the movement is larger that an single assault or attack.
"That they were democratically elected by the Palestinian people, and only through the ballot box will they leave the political scene."
Hamas argues that Israel violated the truce by failing to ease its 18-month blockade on the Gaza Strip.
Egypt's foreign minister has also blamed Hamas for preventing hundreds of wounded Palestinians from entering Egypt via the Rafah crossing for treatment - the only crossing that does not border Israel.
Ahmed Aboul Gheit said the wounded were "barred from crossing" and he blamed "those in control of Gaza" for putting the lives of the injured at risk.
|Barhoum rejected Egypt's statements as an excuse for their 'inaction' towards Israel
But Barhoum denied the accusations, saying that Aboul Gheit was taking advantage of the "massacre and the suffering", to "cover up the state of inaction in Egypt".
Odeh said two lines were being taken on the Palestinian-Israeli issue with Arab states divided between those supporting the Hamas line of armed resistance and not recognising Israel, and those that preferred non-confrontational options.
"More now than ever, they are divided along regional lines of competition of interests in which states are using the Palestinian paper to tug between one another and gain that regional influence.
"There is a lot of anger toward the helplessness and the realisation that in such dire times, Palestinians have been unable to set aside their political differences."
Dozens of tanks and personnel carriers were seen parked at several points near the boundary between Israel and Gaza on Sunday after Israel's defence minister warned it could launch a ground offensive in addition to its air bombardment.
Ehud Barak vowed to "expand and deepen" the bombing raids, unleashed in retaliation for persistent rocket fire into the south of the country from Gaza.
"If it's necessary to deploy ground forces to defend our citizens, we will do so," his spokesman quoted him as saying on Sunday.
The cabinet gave the green light to call up 6,500 reserve soldiers, a senior official told reporters after the meeting.
Jacky Rowland, Al Jazeera's corespondent in Jerusalem, said: "This move gives the Israeli army a lot of leeway to commit troops to this operation as and when they see fit.
"If the fundamental objective of Israel is to change the situation on the ground, clearly they will not be able to do that from the air, they will need to commit ground troops.
"When we look at the full range of air strikes, it does seem that any ground operation would indeed be far-ranging and involve hundreds of troops."