An Israeli strike on a home in Gaza has killed at least 10 people, officials say, as Sunday became the deadliest day since Israel launched an operation against Hamas militants last week.
BBC correspondents say the strike targeted a Hamas official and that a number of children were killed.
PM Benjamin Netanyahu says Israel is ready to expand its operation.
Gaza militants continue to fire rockets at Israel, with injuries reported in towns including Ashkelon and Ofakim.
Sources on both sides say attempts to reach a ceasefire are continuing.
A total of 19 people are reported to have been killed in Gaza by Israeli bombardments so far on Sunday. Of the total, nine were children and four were women, Gaza health officials said.
This brings the death toll in Gaza since Israel launched its Operation Pillar of Defence on Wednesday to 65, the officials said.
Three Israelis were killed on Thursday.
The BBC's Paul Danahar arrived at the scene of the air strike north of Gaza City to see diggers trying to scoop rubble from flattened buildings and with rescuers frantically trying to find survivors.
He says the Hamas man targeted was Mohamed Dalou and that Hamas said nine members of his family had been killed, including a number of children.
Hamas's military wing later said in a statement: "The massacre of the Dalou family will not pass without punishment."
The casualties were taken to Shifa hospital, where earlier our correspondent had seen injured children brought in, one covered in blood.
Our correspondent said the hospital went from organised calm to frantic chaos as doctors tried to dress wounds. One nurse broke down in a corner and colleagues tried to comfort her.
BBC correspondents in Gaza say that seven homes belonging to Hamas officials have been targeted by Israeli strikes on Sunday.
The Israel Defense Forces (IDF) said on Sunday that 55 missiles had been fired into Israel from Gaza, of which 36 were intercepted by its Iron Dome missile defence system.
The Israeli ambulance service reported two people were seriously injured, with 10 moderately or lightly hurt.
Israel's state radio reported that a volley of 10 rockets had been fired at Ashdod, with three falling in a residential area and seven people treated for shock.
One rocket from Gaza made a direct hit on a residential building in Ashkelon, causing injuries and damage.
Another rocket hit a car in Ofakim, causing injuries, the IDF said.
Israel's attacks on Gaza had been stepped up again at about 02:00 (00:00 GMT), with the BBC's Jon Donnison in Gaza City reporting hearing more than a dozen shells, apparently fired from Israeli warships.
Israeli media reported that the head of Hamas's rocket-launching unit, Yehiya Bia, had been killed in a strike.
Two media buildings were struck in Gaza City, injuring eight Palestinian journalists, one of whom had to have have a leg amputated.
Among those using the buildings were a Hamas television channel, al-Quds TV, as well as Sky News and ITN. The BBC had its offices in one of the buildings until last year.
The World Health Organization says hospitals in Gaza are now overwhelmed with casualties and short on supplies.
Palestinian officials say a number of people are still missing under rubble and the total of injured since Wednesday is now 560.
Steps are continuing to try to reach a ceasefire.
Egyptian security officials said a senior Israeli official had arrived in Cairo for talks but Israel has made no comment.
US President Barack Obama, speaking on Sunday, said Washington was "fully supportive of Israel's right to defend itself".
Mr Netanyahu said at a cabinet meeting on Sunday that Israeli soldiers were ready "for any activity that could take place".
"We are exacting a heavy price from Hamas and the terrorist organisations and the Israel Defense Forces are prepared for a significant expansion of the operation," he said.
Egyptian President Mohammed Mursi has said an Israeli ground invasion will have "serious repercussions", saying Egypt would never accept it "and neither will the free world".
The Arab League, which met in emergency session in Cairo, is sending a delegation of foreign ministers to Gaza on Tuesday.
Before the recent offensive, Israel had repeatedly carried out air strikes on Gaza as Palestinian militants fired rockets across the border.
But the aerial and naval bombardment is its most intense assault on the coastal territory since Israel launched a full-scale invasion four years ago.