Palestinian rescuers walk on the rubble of a destroyed Hamas government building following an Israeli airstrike in Gaza City today. Earlier, Israeli aircraft dropped at least 16 bombs on five Hamas government buildings in a Gaza City complex, destroying them, setting fires and sending rubble flying for hundreds of yards, witnesses said. Rescue workers said 40 people were injured.

GAZA CITY, Gaza Strip — Palestinian militants, armed with deadlier missiles than ever before, kept up rocket assaults on Israeli border communities today, despite relentless Israeli air attacks against Gaza's Hamas rulers and unwelcome word from Egypt that it would not bail them out.

More than 370 Palestinians have died since the Israeli air onslaught against Gaza's Islamic Hamas rulers began Saturday, shortly after a rocky, six-month truce expired. Most were members of Hamas security forces but at least 64 were civilians, according to U.N. figures. Among those killed were two sisters, ages 4 and 11, who perished in an airstrike on a rocket squad in northern Gaza today.

Israeli warplanes smashed a Hamas government complex, security installations and the home of a top militant commander. During brief lulls between airstrikes, Gazans tentatively ventured into the streets to buy goods and collect belongings from homes they had abandoned after Israel's aerial onslaught began Saturday.

Rasha Khaldeh, 22, from the central Gaza town of Deir al-Balah, said she dared go no further than down the block to look for food.

"We just don't know what they are going to shell next. It's not safe," Khaldeh said.

The campaign has brought a new reality to southern Israel, too, where one-tenth of the country's population of 7 million has suddenly found itself within rocket range. Militants have pressed on with their rocket and mortar assaults, killing three Israeli civilians and a soldier and bringing a widening circle of targets into their sights with an arsenal of more powerful weapons.

The military estimated that close to 700,000 Israelis are now within rocket range, with the battles shifting closer to Israel's heartland. Of the four Israelis killed since the operation began Saturday, all but one were in areas that had not suffered fatalities before.

"It's very scary," said Yaacov Pardida, a 55-year-old resident of Ashdod, southern Israel's largest city, which was hit Monday. "I never imagined that this could happen, that they could reach us here."

By mid-afternoon, gunmen had launched about a dozen rockets and mortars, down from 80 a day earlier, the Israeli military said. But the number of firings has fluctuated sharply throughout the day, and that number could dramatically rise by day's end.

In the 72 hours since the offensive began, militants have fired more than 250 rockets and mortars all told, they added.

"Zionists, wait for more from the resistance," Hamas spokesman Ismail Radwan wrote in a text message to reporters, referring to militants' armed struggle against Israel.

The offensive comes on top of an Israeli blockade of Gaza that has largely kept all but essential goods from entering the coastal territory since Hamas violently seized control June 2007 from forces loyal to Palestinian President Mahmoud Abbas.

Egypt, which has been blockading Gaza from its southern end, has come under pressure from the rest of the Arab world to reopen its border with the territory because of the Israeli campaign. Egypt has pried open the border to let in some of Gaza's wounded and to allow some humanitarian supplies to enter the territory.

But Egyptian President Hosni Mubarak said in a televised speech today that his country would not throw open the crossing unless Abbas regains control of the border post. Mubarak has been rattled by the presence of a neighboring Islamic ministate in Gaza, fearing it would fuel more Islamic dissidence in Egypt.