Israel has destroyed Hamas' main Gaza security complex in an air strike and is reported to be preparing for a possible invasion of the territory.
More than 280 Palestinians were killed in the first 24 hours of a powerful offensive.
Israeli aircraft are reported to have also bombed the Islamic University in Gaza.
An Israeli army spokeswoman had no immediate comment on the strike. However, witnesses said a series of explosions have hit the Gaza city campus.
Emergency services said militants had fired some 80 rockets into Israel. In one of the deepest attacks, two rockets struck near Ashdod, a main port 30km from Gaza, causing no casualties.
Israeli tanks, deployed on the edge of Gaza, are poised to enter the region where 1.5 million Palestinians live.
Meanwhile, Egypt is trying to broker a ceasefire between Israel and Hamas, Foreign Minister Ahmed Abul Gheit said following talks with Palestinian president Mahmoud Abbas.
Mr Abbas was in Cairo to discuss Egyptian and Arab League efforts to end the violence in Gaza.
Mr Abul Gheit said that a meeting of Arab League foreign ministers set to be held in Cairo on Wednesday should agree on a plan to deal with the crisis that would include seeking a ceasefire and trying to renew a Hamas-Israel truce.
Israel, Hamas and the UN Security Council will be informed of the outcome of Wednesday's meeting, he said.
Egypt brokered a six-month truce between Hamas and Israel which expired last week, heralding a resurgence of tit-for-tat violence that led to Israel's onslaught on the territory.
However, Israeli Defence Minister Ehud Barak has vowed to expand the bombing campaign, pledging that ‘if it's necessary to deploy ground forces to defend our citizens, we will do so,’ his spokesman quoted him as saying.
Mr Abbas, who heads the Palestinian Authority and controls the Israeli-occupied West Bank while his rivals Hamas control Gaza, appealed for Palestinian unity.
He backed Egypt's efforts to broker a new truce, recalling that Arab foreign ministers decided in November that Egypt was the only Arab nation charged with continuing efforts to achieve Palestinian dialogue.
Mr Abbas has blamed the rival Hamas group for triggering Israel's deadly raids on Gaza by not extending a six-month truce with the Jewish state.
Mr Abbas, whose Fatah movement has been at loggerheads with the Islamist group, said maintaining the truce could have helped the Palestinians avoid the Israeli raids.
‘We talked to them (Hamas) and we told them 'please, we ask you, do not end the truce. Let the truce continue and not stop' so that we could have avoided what happened,’ he said in Cairo.
The two groups have been at odds since Hamas won parliamentary elections in 2006 and then drove Fatah forces out of Gaza in June 2007.
Mr Abbas also responded to a defiant statement by the head of the Hamas government in Gaza, Ismail Haniya, that ‘we will not cave in even if (the Israelis) should eradicate Gaza or kill thousands of us’.
‘We reject this logic. We want to preserve every drop of Palestinian blood,’ Mr Abbas said.
Earlier, the UN Security Council called for an immediate end to all military activities in the Gaza Strip and urged the parties to address the humanitarian crisis in the territory.
It comes as Israel has carried out a fresh air strike on a Hamas police station in the northern Gaza Strip this morning.
There were reports of many wounded in the latest raids.
The strike was the latest Israeli hit on the Hamas-run territory, where a massive wave of air strikes marked one of the bloodiest days in the decades-long Israeli-Palestinian conflict.
