Six Palestinians, four of them militants, died in the strikes on Gaza, while a Palestinian civilian was killed in a rocket attack in southern Israel.
The United Nations has called on all sides to show restraint.
The escalation began when an undercover Israeli special forces operation inside Gaza was exposed on Sunday. A Hamas commander was among seven militants killed in clashes, and an Israeli lieutenant colonel in the undercover unit also died.
The incident came after apparent progress in an effort by Egypt and the UN to secure a truce on the Gaza border, where more than 200 Palestinians have been killed in protests since March.
The Israeli military has been accused of using excessive force against protesters, but has said its soldiers have only opened fire in self-defence or on potential attackers trying to infiltrate its territory.
How serious is the latest violence?
After a brief lull following Sunday night’s violence, a barrage of rockets and mortars was launched towards Israel late on Monday, which Israeli medics said killed one person and injured 28.
A bus, which had reportedly been carrying troops, was hit by an anti-tank missile in the Shaar Hanegev region, seriously wounding a…