One rocket slammed into a residential building in the port city of Ashdod more than 30 kilometres (20 miles) from the Gaza border, the Israeli army said.
The army carried out an air strike against the squad that launched the rocket, a spokeswoman said.
Two rockets fell without causing damage or injuries around the desert city of Beersheva some 40 kilometres (24 miles) from the border - the deepest that militant rockets have reached inside Israel.
Another projectile crashed into a factory in the Eshkol region causing damage, it said.
In Gaza, Hamas's armed wing said it fired two rockets at the Hatzerim air force base west of Beersheva. The Israeli army did not comment.
Since the start of Israel's bombardment of Hamas targets on Saturday, militants in Gaza have fired more than 260 rockets and mortars into Israel, killing three civilians and one soldier and wounding several dozen people.
The Israeli offensive has killed at least 400 Palestinians and wounded nearly 2,000 others, according to Gaza medics. -- AFP