Sirens are sounding in Tel Aviv following an explosion, a day after a rocket crashed into the sea off the Israeli city.
The sirens sent people running for cover as TV images showed the Iron Dome anti-missile system firing on an incoming rocket, hitting it in mid-air according to the Israeli military.
The Israeli ambulance service said there were no casualties.
The armed wing of Hamas said it had fired a long-range Fajr-5 rocket at the city.
Earlier on Saturday, four rockets hit the southern city of Ashdod.
Israel's military said on Twitter: "4 rockets fired from #Gaza struck Ashdod: 1 on a house, 1 on a car, 1 near a kindergarten & 1 in an open area."
No-one was killed in the attack.
Before Saturday's rocket attacks, Israel carried out nearly 200 airstrikes on Gaza City overnight
The strikes hit targets in the territory including the Hamas Prime Minister's office, a police compound and a vast network of smuggling tunnels.
Israeli aircraft also kept pounding their original targets, the militants' weapons storage facilities and underground rocket launching sites.
Rocket fire by Palestinian militants into Israel resumed after dawn following a relative lull overnight.
Medics told news agency AFP that eight people died in central and southern Gaza and 30 were injured in the latest strikes.
The latest deaths raised the overall death toll in Hamas-ruled Gaza Strip to 38, as both sides continued to hurl missiles at each other.
Three Israelis have been killed in the recent violence. Four soldiers were also hurt in rocket fire along the southern flank of Israel's border with Gaza, the army said on Saturday.
Israel stepped up its air assault in retaliation to an unprecedented rocket strike aimed at Jerusalem.
Israel's military also called up 75,000 reservists, raising speculation of a ground invasion.
Despite the violence, Tunisia's foreign minister Rafik Abdessalem arrived in the coastal enclave early Saturday in a show of Arab solidarity, heading to a hospital to visit the wounded.
Mr Abdessalem called on the world to help stop Israel's "blatant aggression", and said the Arab League should act as it gathers for talks in Cairo.
Since the start of its operation, Israel's army says militants have fired more than 640 rockets over the border, 410 of which hit Israel, and 230 of which were intercepted by the Iron Dome anti-missile system.
Israeli leaders have threatened to widen Operation Pillar of Defence if the rocket fire from the Gaza Strip does not halt.
Foreign Minister Avigdor Lieberman said options included the possible assassination of Hamas' Prime Minister Ismail Haniyeh and other top leaders.
"Every time that Hamas fires there will be a more and more severe response," he told Israel's Channel 2 TV.
US President Barack Obama has reiterated his country's support for Israel's right to defend itself against rocket attacks from militants in the Gaza Strip.
In a phone call with Israeli Prime Minister Benjamin Netanyahu, Mr Obama also expressed his regret over the loss of Israeli and Palestinian civilian lives, the White House said.
The fighting in Gaza escalated on Wednesday when Israel killed Hamas's military chief in an airstrike.