Hamas militants have launched dozens of rockets at Israel after Israeli air strikes killed senior commanders and felled a multi-storey building in Gaza.
The escalation of the fighting, which began on Monday, has prompted the UN to warn of a "full-scale war".
The conflict has also triggered a wave of street violence in Israel between Jews and Israeli Arabs. Political leaders have appealed for calm.
At least 67 people in Gaza and seven people in Israel have been killed.
For a second day, there was violence in areas of Israel with mixed Jewish and Arab populations. More than 374 people were arrested and 36 officers were injured, Israeli police said.
The fighting erupted on Monday after weeks of rising Israeli-Palestinian tension in East Jerusalem which culminated in clashes at a holy site revered by Muslims and Jews.