(CBS) Israel bombarded the Hamas-ruled Gaza Strip with about 300 airstrikes Saturday and shot down a Palestinian rocket fired at Tel Aviv, the military said, widening a blistering assault to include the Hamas prime minister's headquarters, a police compound and a vast network of smuggling tunnels.

The intensified airstrikes came as Egyptian-led attempts to broker a cease-fire and end Israel's four-day-old Gaza offensive gained momentum. The leaders of Hamas and two key allies, Qatar and Turkey, were in Cairo for talks with Egyptian officials, and the Arab League was holding an emergency meeting.

The White House said President Barack Obama was also in touch with the Egyptian and Turkish leaders. The U.S. has solidly backed Israel so far.

Speaking on Air Force One, deputy national security adviser Ben Rhodes said that the White House believes Israel "has the right to defend itself" against attack and that the Israelis will make their own decisions about their "military tactics and operations."

The Israeli attacks, which Gaza officials say left 12 dead, came as Palestinian militants fired more than 100 rockets toward Israel, including two aimed at the commercial and cultural center of Tel Aviv. Rocket attacks on Tel Aviv and Jerusalem this week mark the first time Gaza militants have managed to fire rockets toward the cities, raising the stakes in the confrontation.

The widened scope of targets brings the scale of fighting closer to that of the war the two groups waged four years ago. Hamas was badly bruised during that conflict, but has since restocked its arsenal with more and better weapons, and has been under pressure from smaller, more militant groups to prove its commitment to fighting Israel.

Militants have unleashed some 500 rockets against the Jewish state.

Correspondent Allen Pizzey reports that, despite vague talk of a cease-fire, Hamas managed to hit a southern Israeli city with four rockets, and retaliation continued unabated.

A massive explosion rocked the Gaza City soccer stadium this morning and speculation was that the target was a rocket launching site. The Israeli bombing campaign expanded into other areas and included the government infrastructure. The cabinet headquarters was flattened.

There were reports of civilians among the casualties. At least half of the Palestinians killed in the conflict so far have been civilians, including at least eight children and a pregnant woman.

In a psychological boost for the Israelis, a sophisticated Israeli rocket-defense system known as "Iron Dome" knocked down one of the rockets headed toward Tel Aviv, eliciting cheers from relieved residents huddled in fear after air raid sirens sounded in the city.

Associated Press video showed a plume of smoke rising from a rocket-defense battery deployed near the city, followed by a burst of light overhead. The smoke trailed the intercepting missile.

Police said a second rocket also targeted Tel Aviv. It was not clear where it landed or whether it was shot down. No injuries were reported. It was the third straight day the city was targeted.

Israel says the Iron Dome system has shot down some 250 incoming rockets, most of them in southern Israel near Gaza.

Saturday's interception was the first time Iron Dome has been deployed in Tel Aviv. The battery was a new upgraded version that was only activated on Saturday, two months ahead of schedule, officials said.

Israel opened the offensive on Wednesday with a surprising airstrike that killed Hamas' military chief, then attacked dozens of rocket launchers and storage sites. It says the offensive is meant to halt months of rocket fire on southern Israel.

While Israel claims to be inflicting heavy damage on Gaza's Hamas rulers, it has failed to slow the rocket fire. In all, 42 Palestinians, including 13 civilians, have been killed, while three Israeli civilians have died.

Isreal Bombards Gaza Strip, Shoots Down Rockets