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."
"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," Mr. Rhodes told reporters on Air Force One en route to Asia.
Hamas health officials said 45 Palestinians had been killed and 385 wounded since Wednesday's escalation in the cross-border battle. In Israel, 3 Israeli civilians have died and 63 have been injured. Four soldiers were also wounded on Saturday.
Two rockets were fired at Tel Aviv on Saturday. One landed harmlessly, probably at sea. The other was intercepted by the Iron Dome defense system in the sky above the city. An Iron Dome antimissile battery had been hastily deployed near the city on Saturday in response to the threat of longer-range rockets.
Since Wednesday, Iron Dome has knocked 245 rockets out of the sky, the military said, while 500 have struck Israel. The American-financed system is designed to intercept only rockets streaking toward towns and cities and to ignore those likely to strike open ground.
There have been failures -- on Saturday a rocket crashed into an apartment block in the southern port city of Ashdod, injuring five people -- but officials have put its success rate at 90 percent.
Analysts said there is no clear end to the conflict in sight, 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," said Efraim Halevy, a former chief of Israel's intelligence service, "both sides want Hamas to remain in control, strange as it sounds."
But Mkhaimar Abusada, a political science professor at Al Azhar University here, cautioned that "there is no military solution to the Gaza problem."
"There has to be a political settlement at the end of this," he said. "Without that, this conflict is just going to go on and on."
President Mohamed Morsi of Egypt said late Saturday night 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, the Qatari prince, 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. Hamas -- which won elections in Gaza in 2006 and took full control in 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 seeks Israel's withdrawal from the 1,000-foot buffer it patrols on Gaza's northern and eastern borders.
Mr. Rhodes said the Turkish and Egyptian leaders "have the ability to play a constructive role in engaging Hamas and encouraging a process of de-escalation."
Mr. Netanyahu, for his part, spoke with the leaders of Britain, Germany, Italy, Greece, Poland, Portugal, Bulgaria 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.
The Israeli assault continued early Sunday, with bombs fired from the air and the sea hitting Gaza City. One attack injured several journalists at a communications building, witnesses said, and Palestinian news agencies reported that two children were killed in a predawn strike in Beit Lahiya.
A statement from the Israeli military said it had "targeted dozens of underground launchers," and also hit Saraya, which it described as a Hamas training base and command center. The navy attacked "terror sites on the northern Gaza shore line," the statement said, and repeated rounds of missiles could be easily heard from the Al Deira Hotel, on the seashore, where many foreign journalists are staying.
Israel's stated goals for the operation are to reclaim calm for its residents, deter further rocket attacks and cripple Hamas's military capabilities. 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."
The military said that, in addition to the Hamas prime minister's office, it also struck the police and homeland security headquarters. But Mr. Regev said the expansion of the assault to government buildings did not indicate a shift in strategy.
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."
While Israeli domestic support for the offensive remained strong, a debate has begun about when and how to bring the operation to an end.
Yisrael Ziv, a former head of operations for the Israeli military, said Saturday that as the number of targets reachable from the air shrank, Israel may soon "have to go in on the ground," but cautioned that the move presents greater risks. "You have to know how far not to go," he said on Israeli television.
But Tzachi Hanegbi, a former chairman of the Israeli Parliament's Foreign Affairs and Defense Committee, said, "We are in a very early stage of the operation," adding: "I wouldn't start talking about exit strategies at this point."
The 4 a.m. strike on Mr. Haniya's office was as much a psychological blow as a tactical one. A singed copy of the official Palestinian book of laws lay amid the pile of rubble, along with datebooks and personnel records listing the bank accounts for depositing police officers' paychecks. Mr. Haniya's gray-bearded face beamed from a page in Hamas's signature green: the cover of a 2008 booklet declaring "the government's achievements despite the obstacles."
Just before 10 a.m., a security official who worked at the building and asked to be identified only as Abu El Abed planted a Palestinian flag in the debris, declaring, "We will rebuild this place as we have rebuilt others."
He added: "But the blood of anybody wounded is more important than any structure."
Israel's military said that it also bombed smuggling tunnels under Rafah 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. Mr. Salah and his family were not in the house, but 30 people were wounded as the surrounding homes were damaged or destroyed.
Dozens of people, many of them children, swarmed over the rubble pile, where clothing and a bottle of detergent sat along with remnants of lights and furnishings. Hassam Al Dadah, 41, loaded a truck with mattresses, blankets, a refrigerator, couch cushions and a child's doll.
Mr. Dadah, a teacher, said his five children, ages 6 to 14, were being treated at the hospital, and he did not know where the family would spend the night. "I'm a new refugee," said Mr. Dadah. "I don't have any place to go to."
Jodi Rudoren reported from Gaza City, and Isabel Kershner from Jerusalem. Reporting was contributed by Fares Akram and Tyler Hicks from the Gaza Strip, Carol Sutherland and Iritz Pazner Garshowitz from Jerusalem, and David D. Kirkpatrick and Mayy El Sheikh from Cairo.
This article originally appeared in The New York Times.