GAZA CITY, Gaza Strip — 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.