Hamas's armed wing, the Ezzedine Al-Qassam Brigades, has said it fired four rockets at Tel Aviv and one at the northern port city of Haifa in response to Israel's destruction of two residential towers in Gaza.
Israeli website Yedioth Ahronoth said on Tuesday that at least 130 rockets were fired at Israel and that the Iron Dome, Israel's air defence system, was able to counter only 60 of them.
Israeli air strikes on Gaza City killed two Palestinians early Tuesday, while scores more were wounded when warplanes bombed two high-rise residential blocks, medics and witnesses said.
Witnesses said that F16s fired at least six rockets at the tower block, which has 60 apartments and a commercial complex including dozens of shops, completely destroying it.
They said residents fled the building after the Israeli army sent them pre-recorded warning messages.
Meanwhile, AFP reported that the Israeli army confirmed carrying out 15 air strikes since midnight (2100 GMT Monday), claiming that among them buildings serving as Hamas "command and control centres."
"Our forces also attacked compounds in two schools in the central and northern Gaza Strip that served as centres for terror activity from which low-trajectory fire was directed at Israel," a statement claimed.
During the night, there was no rocket fire on Israel, but at 6:30am (0330 GMT), militants fired a heavy barrage over the border, setting sirens sounding all up the Mediterranean coast, the Israeli army said.
Since then, 21 rockets have been fired at Israel, 18 of which struck the south and one of which was intercepted over greater Tel Aviv, a spokeswoman said.
Two people wounded previously died of their injuries on Monday, raising the Gaza death toll since the 8 July start of the campaign to 2,135 with 10,915 wounded, according to the emergency services.
On the Israeli side, 68 people have been killed, the vast majority soldiers.
She said there were no reports of anything hitting farther north than the southern port city of Ashkelon where a rocket hit a house causing major damage and lightly wounding 21 people.
Late on Monday, two rockets fired from Lebanon hit northern Israel, an Israeli army spokeswoman said.
Media reports pointed out on Monday that Egypt is currently exerting diplomatic efforts to reach a new ceasefire agreement between the Palestinian resistance factions and Israel.
Last week, Israeli and Palestinian groups blamed one another for the collapse of an Egyptian-sponsored 24-hour truce late on Tuesday, which led to the resumption of the Israeli offensive against Gaza.