Palestinian militants have fired more than 430 rockets into Israeli territory since Saturday. Israel says most were intercepted but one man was killed.
The Israel Defense Forces (IDF) say they have struck about 200 targets in the Gaza Strip over the weekend.
The Palestinians say four people were killed in those strikes.
The flare-up comes despite a truce agreed last month. Egypt and the United Nations have recently been trying to broker a longer-term ceasefire.
It began on Friday, during protests in Gaza against the blockade of the area - which Israel says is needed to stop weapons reaching militants.
A Palestinian gunman shot and wounded two Israeli soldiers at the boundary fence. Israel retaliated with an air strike that killed two militants.
The rocket barrage from Gaza began on Saturday morning. Israel's Iron Dome missile defence system shot down dozens of the rockets, but a number of homes in Israeli towns and villages were hit.
An Israeli man died early on Sunday in Ashkelon, 10km (six miles) north of Gaza, after being struck by shrapnel in his home.
Israel says it killed two Palestinian fighters in air strikes against sites belonging to the militant groups Hamas and Islamic Jihad on Saturday and Sunday.
But Hamas, which controls Gaza, says a total of four Palestinians have been killed.
It says the dead include a woman and her 14-month-old daughter. But Israel says the mother and baby may have been killed by a Palestinian rocket that fell short of its target.
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