Khaled Meshaal, the exiled Hamas leader living in Syria, also denounced the Israeli attacks against Gaza's civilians as "the real holocaust".
Abbas later requested an emergency meeting of the UN Security Council to discuss the Israeli incursion into the Gaza Strip, a spokesman for the Palestinian leader said.
Marwan Bishara, Al Jazeera's senior political analyst, said that "at best" Abbas could hope to get a Security Council resolution condemning the Israeli action.
"And as we know, Israel has ignored tens of UN Security Council resolutions over the last 40 years, and hundreds of UN assembly resolutions - so this is going to be more talk and probably not much will come out of it in the end," he said.
Rana el-Hindi from Save the Children, speaking from inside the Gaza Strip, told Al Jazeera children were suffering greatly from the Israeli bombardment.
"In the last three days at least 19 children have been killed ... it's a real concern for all organisations here," she said.
"Most of the time, when we go into the field and talk to the children about their fears and concerns, they are always afraid of a new [Israeli] invasion to the Gaza Strip - and obviously the current situation is just ... what they fear."
She said the number of children being hospitalised was increasing "day after day".
Eissam Younis, director of the Al Mizan Centre for Human Rights in Gaza, told Al Jazeera that the Israeli army was "intentionally and systematically targeting civilians" and criticised world powers for their muted response.
"Israel puts itself above the law because the international community is always silent," he said.
The latest attacks mark the fourth day of Israeli bombardment and follow the death of an Israel civilian in a Palestinian rocket attack.
Those killed in Saturday's attacks included at least eight civilians, four of them women, said Dr Muawiya Hassanein, head of Gaza's emergency services
At least 15 of those killed were fighters, including 10 fighters from Hamas and two from the Islamic Jihad.
An operation in the Jabaliya refugee camp on Saturday marked the deadliest day of fighting in the Hamas-ruled territory for more than a year.
Witnesses said the Jabaliya deaths occurred as a result of gun battles between Palestinian fighters and Israeli soldiers.
Tariq Dardouna, a Palestinian resident trapped in his house in east Jabaliya, told Al Jazeera that Israeli forces targeted civilians.
"The Israeli army opens fire at everything in our area, including children and houses. There are injured children bleeding inside their houses," Dardouna said.
"They are opening fire at everything."
Witnesses also reported clashes in the nearby Tufah neighbourhood in northern Gaza City.
The Israeli army confirmed its operations in northern Gaza, with the Israel Army Radio reporting that five Israeli soldiers were wounded in the fighting.
Threat of invasion
There has been increasing domestic pressure in Israel to mount a full-scale invasion of the Gaza Strip.
Ehud Barak, Israel's defence minister, said on Thursday that "a major ground operation was real and tangible" and that Israel was "not afraid of it".
Senior Palestinian officials have told Al Jazeera that the peace negotiations begun in Annapolis last year, could be at risk if the Israeli military assault on Gaza continues.
Tzipi Livni, the Israeli foreign minister who heads the Israeli negotiation team, reacted by saying that the Israeli military action would be unaffected by any suspension of the peace talks.
"Even if the Palestinians suspend talks, it won't influence in any way the decisions or operations Israel carries out to defend its citizens," she said.
In Israel, six people were wounded, one of them seriously, by long-range rockets fired from the Gaza Strip on Saturday, the Israeli army said.
Fighters in Gaza fired over 40 rockets and mortars at southern Israel.
Eight of the missiles were long-range rockets that travelled as far as the seaside Israeli town of Ashkelon, some 11km north of the Gaza Strip.
Israel's political and military leadership has been considering a major ground offensive in the Hamas-ruled territory to prevent fighters from deploying more long-range rockets like those that hit Ashkelon.
Palestinian fighters have launched frequent volleys of rockets and mortars at Israeli communities near the Gaza border, though the missile attacks rarely cause injuries.
Source: Al Jazeera and agencies