Eight members of Palestinian family, including five children, among 88 dead so far, with no casualties on Israeli side.
Israeli warplanes kept up deadly raids on Gaza but failed to stop rocket fire across the border, as the United States offered to help negotiate a truce.
As the violence worsened, US President Barack Obama said his government was willing to broker a ceasefire in a phone call to Israeli Prime Minister Benjamin Netanyahu.
Obama said he was concerned the fighting could escalate and “called for all sides to do everything they can to protect the lives of civilians”, the White House said.
At least 88 Palestinians, most of them civilians, have been killed in Israeli bombardment of the Gaza Strip, Palestinian officials say, as talk of a possible Israeli ground offensive gathers momentum.
In the deadliest attack since the start of the invasion on Tuesday, eight Palestinian family members, including five children, were killed in an early-morning air raid that destroyed at least two homes in Khan Younis, in southern Gaza, the Palestinian Health Ministry said on Thursday.
Al Jazeera’s John Hendren, reporting from Gaza, said though there were two sides to the conflict, the result of the violence was lopsided.
On the Palestinian side, at least 88 people have been killed and hundreds of others wounded, while there have been no reports of casualties in Israel besides two injuries.
The clashes and exchange of rocket fire between Hamas and Israeli mlitary has drawn strong reactions from leaders across the globe.
Ban Ki-moon, UN secretary-general, briefed the Security Council on the crisis on Thursday. He condemned the rocket attacks and urged Israel to show restraint.
Al Jazeera’s James Bays, reporting from the UN in New York, said it was unlikely the Security Council would release anything more than a “carefully worded statement” on the matter.
Medical officials in Hamas-ruled Gaza said at least 60 civilians, including a four-year-old girl and boy aged five who were killed on Thursday, were among the 88 Palestinians killed.
In a statement, the Israeli army said: “During the [ongoing military] operation, the IDF has struck a number of houses throughout Gaza that were being used for military purposes. … These houses may be used for weapons storage, command and control centre, or communications.”
The Israeli offensive began after a build-up of violence following the killing of three young Israeli settlers last month and the murder of a Palestinian teen in a suspected revenge attack.
Israel says it has struck more than 750 targets in Gaza and that its air offensive is intended to halt persistent rocket fire at its own civilian population, which escalated after Israeli forces arrested hundreds of Hamas activists in the occupied West Bank following the abduction of the Jewish teenagers.
It accuses Hamas of deliberately putting innocent Palestinians in harm’s way by placing weaponry and fighters in residential areas.
The wail of air raid sirens has paralysed business i southern communities in Israel and sent hundreds of thousands of people scrambling for shelter in Tel Aviv.
Two rockets were shot down on Thursday, but offices and shops remain open and roads are clogged with traffic.
Israeli leaders, who have popular support for the Gaza action, have also warned the air offensive could be expanded into a ground invasion of one of the world’s most densely populated territories. Some 20,000 reservists have been mobilised, the military says.
“Everyone in Gaza is talking about a ground invasion and people are saying that is the next step,” Al Jazeera’s Hendren said.