The military wing of Hamas has vowed that Israel will pay a "tremendous price" for the air strikesThe situation in Gaza "is on a knife-edge", UN Secretary General Ban Ki-moon has said, urging Israel and Palestinian militants to end hostilities.
Mr Ban warned that the region "cannot afford another full-blown war".
His comments came after Israel said Hamas had fired dozens of rockets at Israeli cities on Wednesday night, following Israeli air strikes in Gaza.
More than 60 Palestinians are reported to have died since Tuesday in Israeli air strikes against militants.
Gaza medical officials say half of the casualties were civilians, including women and children.
Eight Palestinians were killed in an air raid on a house near the southern town of Khan Younis early on Thursday, the Palestinian health ministry said.
An Israeli military spokesman said the deaths were "a tragedy - not what we intended", as people had returned to the building too soon following a telephone warning.
Another nine people were reported killed in a strike on a cafe in the same town.
"The deteriorating situation is leading to a downward spiral which could quickly get out of control," Mr Ban said.
"The risk of violence expanding further still is real."
He demanded that Hamas militants stop firing rockets and also urged the Israeli government to exercise restraint and respect international obligations to protect civilians.
The UN Security Council is due to meet for emergency talks on the crisis later on Thursday.
Israeli PM Benjamin Netanyahu earlier vowed to "further intensify attacks on Hamas" in Gaza, saying the militants would "pay a heavy price" for their rocket attacks.
"This operation could take time. We are resolved to defend our families and our homes," he said.
Israel says its targets have been militant fighters and facilities including rocket launchers, weapons stores, tunnels and command centres.
Mustafa Barghouti, a member of the Palestinian Legislative Council, accused Mr Netanyahu of "preparing a ground operation which could bring a huge massacre in Gaza".
He told the BBC that Hamas was ready for a mutually declared ceasefire, but that Israel had rejected a truce. "Mr Netanyahu seems determined to continue this terrible war," Mr Barghouti said.
Israeli President Shimon Peres told CNN that a ground offensive might happen "quite soon". The army has called up about 40,000 reservists.
The military said its Iron Dome missile defence system had intercepted 21 of the 82 rockets fired on Wednesday, including three above Tel Aviv, three over Ashkelon and three over Ashdod.
Israel has carried out more than 230 air strikes since Tuesday, hitting nearly 600 targets as part of its operation Protective Edge.
Hamas said that all Israelis were now targets, accusing Israel of violating the Egyptian-brokered truce that ended exchanges in 2012.
'Forced upon us'
The leaders of France and Germany condemned the attacks on Israel after speaking to Mr Netanyahu.
Senior US officials urged "all sides to de-escalate the situation", a state department spokeswoman said.
But the leader of Hamas' political bureau, Khaled Meshaal, warned that Hamas would continue to retaliate and called on Palestinians to unite.
He also criticised what he described as the international community's lack of support for the Palestinian people.
"This war was forced upon us," he said in a televised speech on Wednesday.
Last month, Hamas and Mr Abbas formed a unity government to end a major rift between factions in the West Bank and Gaza.
Israel suspended crisis-hit peace talks with the Palestinians in April in response to the announcement of the reconciliation deal.
Tensions rose last week with the murders of three young Israelis in the occupied West Bank and a Palestinian teenager in Jerusalem.
Israel says Hamas was behind the abduction and murder of the Israeli youths - a claim it denies.
A day after their funerals, the Palestinian youth was abducted in East Jerusalem and murdered. Police have arrested six Jewish suspects and say it seems the 16-year-old was killed because of his nationality.