GAZA CITY, Gaza Strip — Israel broadened its assault Saturday on the Gaza Strip 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.

The attack, one of several on government installations, happened a day after the prime minister, Ismail Haniyeh, hosted his Egyptian counterpart in that very building, a sign of Hamas’ growing legitimacy in the 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 possible ground invasion, the conflict showed no sign of abating. Gaza militants again fired long-range missiles at the population center of Tel Aviv, among nearly 160 launched into Israel on Saturday, injuring five civilians in an apartment build- ing in Ashdod, in southern Israel, and four soldiers in an unidentified location. The launches raised the number of rockets fired into Israel in four days to about 500.

Israel said it carried out more than 300 airstrikes Saturday, including afternoon strikes on a Hamas commander’s home in the Gaza City neighborhood of Zeitoun and on a motorcycle-riding militant in the southern border town of Rafah. Israel also has made preparations for a possible ground invasion.

Hamas health officials said 46 Palestinians, including 15 civilians, had been killed and more than 400 civilians had been wounded since Wednesday’s escalation in the crossborder battle; three Israelis have died and more than 50 civilians have been injured.

In a psychological boost for Israel, a new rocket-defense system known as “Iron Dome” knocked down a rocket headed toward Tel Aviv, eliciting cheers from relieved residents huddled in fear after air-raid sirens sounded in the city.

Israel says the Iron Dome system shot down about 250 of 500 rockets fired toward the country last week, most in southern Israel near Gaza.

Saturday’s interception was the first time Iron Dome has been deployed in Tel Aviv. The battery was an upgraded version that was activated Saturday, two months ahead of schedule, the Defense Ministry said.

“Everybody is afraid of what’s next,” said Mkhaimar Abusada, a political science professor at Al-Azhar University in Cairo, predicting that the rockets fired at Tel Aviv and, on Friday, at Jerusalem, would provoke a rerun of Israel’s ground invasion four years ago.

Israel’s defense minister, Ehud Barak, has authorized the emergency call-up of up to 75,000 reserve troops ahead of a possible ground offensive. Israel has massed thousands of troops and dozens of tanks and armored vehicles along the border in recent days.

Abusada and Efraim Halevy, a former head of Israel’s intelligence service, both said there is no clear endgame to the conflict, since Israel neither wants to re-engage in Gaza nor to eliminate Hamas and leave the territory to the chaos of more militant factions.

“Ultimately,” Halevy said, “both sides want Hamas to remain in control, strange as it sounds.”

But Abusada cautioned that “there is no military solution to the Gaza problem,” saying: “There has to be a political settlement at the end of this. Without that, this conflict is just going to go on and on.”

President Mohammed Morsi of Egypt said late Saturday that “there could be a cease-fire soon,” after he and other members of his government spent the day in meetings with the Turkish premier, Recep Tayyip Erdogan, the Qatari prince, and the political leaders of Hamas and other Gaza factions. But Mark Regev, a spokesman for Prime Minister Benjamin Netanyahu of Israel, denied reports that a truce was imminent.

It was unclear whether the deal under discussion would solely suspend the fighting or include other issues.

In a speech Saturday at Cairo University, Erdogan vowed support for Palestinians in the Gaza Strip.

Hamas, which has controlled the Gaza Strip since 2007 but is considered a terrorist organization by Israel and the United States, wants to turn its Rafah crossing with Egypt into a free-trade zone and wants Israel to withdraw from the 1,000-foot buffer it patrols on Gaza’s northern and eastern borders.

The Brotherhood official said the Israeli side of the talks remained “the sticking point,” though he would not be specific about the issues.

Ben Rhodes, President Barack Obama’s deputy national security adviser, said the president had spoken daily with Netanyahu since the crisis began, as well as to Erdogan and Morsi.

“They have the ability to play a constructive role in engaging Hamas and encouraging a process of de-escalation,” Rhodes said of the Turkish and Egyptian leaders. Describing rocket fire coming from Gaza as “the precipitating factor for the conflict,” he added, “We believe Israel has a right to defend itself, and they’ll make their own decisions about the tactics that they use in that regard.”

But the Tunisian foreign minister, standing outside Al-Shifa Hospital in the Gaza strip, said Israel “has to respect the international law to stop the aggression against the Palestinian people.”

Netanyahu spoke Saturday with the leaders of Germany, Italy, Greece and the Czech Republic, according to a statement from his office.

Lt. Gen. Benny Gantz, chief of the Israeli military, met with his top commanders and instructed his troops “to continue attacking with full force in the Gaza Strip and to increase the rate of attacks on terrorist targets,” according to a military statement. A senior military official said Israel had hit nearly 1,000 sites since Wednesday in what he called “intelligence-driven precision strikes,” and described civilian casualties as “regrettable” but unavoidable because the “terrorist infrastructure is embedded inside the population.”

Israel’s stated goals for the operation are reclaiming calm for its residents, deterring further rocket attacks and crippling Hamas’ military capabilities. The expansion of the assault to government buildings suggested Israel may be running out of targets relating to the long-range rockets that present the greatest threat, but Mark Regev, Netanyahu’s spokesman, played down the idea that new attacks represented a shift.

Hamas “makes no distinction between its terrorist military machine and the government structure,” he said. “We have seen Hamas consistently using so-called civilian facilities for the purposes of hiding their terrorist military machine, including weapons.”

After the 4 a.m. strike on Haniyeh’s office, a singed copy of the official Palestinian book of laws lay in the huge pile of rubble the building was reduced to, along with datebooks and personnel records listing the bank accounts for depositing police officers’ paychecks.

Missiles also smashed into two small security facilities and the Hamas police headquarters in Gaza City, setting off a huge blaze that engulfed nearby houses and civilians’ parked cars, the Interior Ministry reported. No one was inside the buildings.

Air attacks knocked out five electricity transformers, cutting off power to more than 400,000 people in southern Gaza, according to the Gaza electricity distribution company. People switched on backup generators for limited electrical supplies.

Just before 10 a.m., a security official who worked at the prime minister’s office building and asked to be identified only as Abu El Abed planted a Palestinian flag in the rubble, declaring, “We will rebuild this place as we have rebuilt others.

“Every structure that is demolished or destroyed is a big loss,” he said. “But the blood of anybody wounded is more important than any structure.”

Israel’s military on Saturday also bombed smuggling tunnels under Rafah that militants use to smuggle in weapons and other contraband from neighboring Egypt and carried out what it described as pinpoint strikes of Hamas commanders.

One such attack flattened the home of Ibrahim Salah, head of public relations for the Hamas Interior Ministry, in the Jabaliya refugee camp, one of the most densely populated areas in the world. Salah and his family were not in the house, but Hamas officials said the strike wounded 30 neighbors and damaged or destroyed several of the surrounding homes.

Information for this article was contributed by Jodi Rudoren, Isabel Kershner, Fares Akram, Tyler Hicks, Carol Sutherland, Iritz Pazner Garshowitz, David D. Kirkpatrick and Mayy El Sheikh of The New York Times and by Ibrahim Barzak, Josef Federman, Karin Laub, Jim Kuhnhenn and Aya Batrawy of The Associated Press.

Front Section, Pages 1 on 11/18/2012