Israel has been attacked by more than 80 rockets, including at least 30 in just an hour late on Monday evening, according to the Israeli army.
Hamasmilitants launched “several dozen rockets” within a short period of time, the Israel Defence Forces said.
There are so far no reports of casualties.
The rocket fire was claimed by Hamas’ armed wing, the Ezzedine al-Qassam Brigades, in a statement sent to the AFP news agency in Gaza.
At least four of the rockets were intercepted over Netivot by the Iron Dome anti-missile system, the Israeli army said.
Another 16 struck the area around the southern city of Beersheva, 25 miles from Gaza, and home to 200,000 people, the army added.
The IDF said a total of 80 rockets had been fired at Israel over the past 24 hours.
The rocket bombardment came a few hours after Israel launched 16 air strikes on targets in Gaza, and followed a night where planes attacked 14 targets, killing at least three militants.
Another five died after a tunnel collapsed near the city of Rafah, with Hamas blaming it on an Israeli air strike – a claim which they deny.
Witnesses told AFP that the Israeli air force had responded to the latest rocket attack by hitting some 30 targets near Rafah.