Palestinian officials said three Palestinians were killed in Israeli attacks since Wednesday: a member of the Islamist Hamas group that rules Gaza, a pregnant woman, and her 18-month-old child.
At least five Palestinian civilians were wounded, local medical officials said.
As fighting entered a second day on Thursday despite efforts to broker a truce to end months of simmering violence, Palestinians fired dozens of rockets into southern Israel and Israel launched scores of air strikes in Gaza
The Israeli military said seven people were wounded in southern Israel; one was identified by her employer as a Thai agricultural worker.
The rocket fire from Gaza has not targeted Israel's heartland and the Israeli military said its air strikes were limited to Hamas installations.
Hamas spokesman Sami Abu Zuhri blamed Israel for the escalation, citing the killing of two Hamas gunmen on Tuesday in northern Gaza which he described as unprovoked.
Israeli media reports said fire from the gunmen had apparently been part of a Hamas exercise and not directed at Israel.
An Israeli military spokesman said Hamas operatives had shot in the general direction of Israel's border.
Yuval Steinitz, a member of Prime Minister Benjamin Netanyahu's inner cabinet, told Israel Radio: "We are not eager for war and are not interested in a broader confrontation but at the same time it could certainly happen because we will not make any concessions to Hamas."
Netanyahu was due to convene the security cabinet later to assess the situation.
The flare-up came after officials on both sides had talked about potential progress in an effort by the United Nations and Egypt to broker a truce to end months of violence and alleviate deepening humanitarian and economic hardship in the Israeli-besieged Gaza Strip.
Rocket warning sirens sounded almost non-stop in the southern Israeli town of Sderot and other border communities from sunset on Wednesday. Many residents have a reinforced room in their homes where they can shelter. The military said more than 150 rockets and mortar bombs were fired from Gaza.
Ambulance sirens echoed through the night in Gaza, where families huddled at home as powerful explosions shook buildings. The Israeli military said its aircraft struck 140 facilities belonging to Hamas.
U.N. Middle East envoy Nickolay Mladenov said in an overnight statement: "I am deeply alarmed by the recent escalation of violence between Gaza and Israel, and particularly by today’s multiple rockets fired towards communities in southern Israel."
The United Nations, he said, has engaged with Egypt in an "unprecedented effort" to avoid serious conflict, but cautioned that "the situation can rapidly deteriorate with devastating consequences for all people".
*This story was edited by Ahram Online