GAZA CITY — Israel broadened its assault on the Gaza Strip on Saturday from mostly military targets to centers of government infrastructure, obliterating the four-story headquarters of the Hamas prime minister with a barrage of five bombs before dawn.

The attack, one of several on government installations, came a day after the prime minister, Ismail Haniya, hosted his Egyptian counterpart in that very building, a sign of Hamas’s new legitimacy in a radically redrawn Arab world. That stature was underscored Saturday by a visit to Gaza from the Tunisian foreign minister and the rapid convergence in Cairo of two Hamas allies, the prime minister of Turkey and the crown prince of Qatar, for talks with the Egyptian president and the chairman of Hamas on a possible cease-fire.

But as the fighting ended its fourth day, with Israel continuing preparations for a ground invasion, the conflict showed no sign of abating. Gaza militants again fired long-range missiles at Tel Aviv, among nearly 60 that soared into Israel on Saturday. Israel said it hit more than 200 targets overnight in Gaza, and continued with afternoon strikes on the home of a Hamas commander and on a motorcycle-riding militant.

The White House reiterated its strong support for Israel, with Ben Rhodes, the deputy national security adviser, describing rocket fire from Gaza as “the precipitating factor for the conflict.”