Israel hopes the onslaught will greatly reduce the number of missiles fired from Gaza onto Israeli towns, and also erode support for Hamas.
The Islamist movement won elections in Gaza in 2006 before seizing control of the coastal strip a year later, ousting its secular Palestinian rival Fatah, which now holds sway in parts of the West Bank.
On Sunday the home of Ahmed Jabari, the head of Hamas's military wing, was destroyed in an air strike at Shujaia, a suburb of densely-populated Gaza City, according to the Israeli military.
Israel said its warplanes had also bombed sites on the Egypt-Gaza frontier near the town of Rafah, including a mosque allegedly used as a weapons storage depot and militant training camp.
Its ground forces were involved in a "number of incidents", the Israeli military said.
The strikes came hours after Israel dropped leaflets and left phone messages warning Gazans to stay away from areas used by Hamas and saying its operation would soon enter "phase three".
Hamas launched a barrage of rockets on Sunday, two of which struck 42 km (26 miles) inside southern Israel at the city of Beersheba, the military said. There were no reported casualties or damage.
Some 820 Gazans and 13 Israelis have reportedly died in 14 days of fighting. Medical staff said 235 children were among the Palestinians dead.
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