Israel said about 50 rockets had been fired from Gaza yesterday and another 20 today, although no injuries have been reported.
Among the dead were three women, one of them heavily pregnant, and seven children. That number includes the woman's unborn baby, whom medics tried but ultimately failed to save, medics said.
The violence resumed at around yesterday when three rockets struck southern Israel with the Israeli air force hitting back with strikes which continued through the night and into today.
Shortly before dawn, an air strike hit a home in Deir al-Balah in central Gaza, killing eight, among them the pregnant woman, her unborn baby, three children and three men.
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Later in the morning, another child, 4, was killed along with a man in his 20s in a strike on Zeitun in southern Gaza City, Qudra said.
Separately, a man died of injuries sustained earlier in the conflict, which erupted on July 8.
The hostilities resumed hours before a temporary ceasefire was due to expire.
Talks in Egypt's capital to end the violence broke up without a deal. Israeli delegates said they would return home.
It was not known whether Deif had survived last night's attack, although Hamas' exiled deputy leader Mussa Abu Marzuk was quoted as saying in Cairo that two of the victims were his wife and daughter, the BBC reported.
Israeli Interior Minister Gideon Saar told army radio that he was a "legitimate target" and that if an opportunity arose to eliminate him, it should be taken.