ASHDOD, Israel — A piercing shriek went up and a young woman fainted as the body, wrapped in a white shroud, was brought into the packed funeral hall.

On Tuesday, this fast-developing, modern port city about halfway between Gaza and Tel Aviv buried its first victim of a rocket attack: Irit Sheetrit, a 39-year-old mother of four.

The Katyusha-type rocket that killed her was fired Monday night by Palestinian militants from Gaza. It was the first to have hit this city of more than 200,000, about 18 miles north of the Palestinian territory, and underscored how rockets from Gaza were reaching farther into the country with each passing day.

As the sun set on Tuesday, rockets flying out of Gaza were landing in new places, like Kiryat Malachi, to the northeast, and Beersheba, a major city in Israel’s south.

Over the weekend, Israel began its devastating aerial bombardment of Hamas targets in Gaza with the stated goal of stopping the incessant rocket fire that has plagued Israeli towns and villages close to the border for years.

More than 370 Palestinians have been killed in the Israeli assault so far, Palestinian officials said. Among the dead were at least 62 women and children, according to the United Nations, and an unknown number of civilian men. The militants have responded by firing increasingly advanced rockets with longer ranges into Israel.

Yet here, amid the sobbing of the mourners, many of them in a state of shock and disbelief, support for a sustained Israeli military campaign remained strong.

“Of course we support it,” said Rosette Alalouf, a former colleague of Ms. Sheetrit, at the funeral. “Do we have a choice?”

In his eulogy, Yehiel Lasri, the mayor of Ashdod, conveyed the prevailing spirit of resolve here. “Has not the time come to use full force and all the means at our disposal?”

Mr. Lasri added that he had watched as Sderot first came under rocket fire, then Ashkelon, a city on the coast. “We hoped they would not get to Ashdod, but we did not delude ourselves,” he said, noting that the authorities had been preparing for such a situation for two years.

The ability of civilians to withstand heavy rocket fire, which Israel fully expected in the wake of its campaign, is a crucial part of the military equation. As Prime Minister Ehud Olmert of Israel put it at the weekly cabinet meeting on Sunday, “The patience, determination and stamina of the residents of the home front will, in the end, determine the ability” of Israel to attain its military and diplomatic goals.

Israeli officials say the preparations in that home front — which now includes hundreds of thousands of citizens in southern Israel — have saved many lives. Though four Israelis have been killed in rocket attacks since the start of the military operation, three of them on Monday, officials say the hundreds of rockets that have been fired could have exacted a much heavier toll.

All communities within 25 miles of Gaza have sirens that serve as alerts for incoming rockets, and while the Hanukkah vacation officially ended on Tuesday, schools within the range of the rockets remained closed.

Television and radio stations repeatedly broadcast instructions on how to behave during an alert. Those driving, for example, are told to get out of their cars and lie on the ground.

Ms. Sheetrit had been on her way home from the gym with her sister when the siren wailed. She managed to get out of the car and tried to take shelter in a bus station, but the rocket slammed down too quickly, too close.

The impact site has turned into something of a local destination. Curious residents came by on Tuesday, some taking photographs on their cellphones. A group of children from a nearby apartment building searched a grassy verge for tiny metal balls and other bits of shrapnel that had scattered all around.

Two more rockets hit Ashdod in the evening, this time falling in open areas and causing no harm.

The center of town was unusually quiet on Tuesday, though stores remained open in an attempt to maintain a sense of normality. Many of the adults seemed reconciled to the new situation, but they said that the children were very afraid.

Zion Ben Abu, 45, the owner of a falafel shop, said he used to run a factory in an industrial zone on the Gaza border where dozens of Palestinians worked. He said he felt some sympathy for average Gazans, who “mostly want to send their kids to school and live quietly, like us.”

The problem, he said, is the Hamas leaders, who had left Israel no choice but to fight.

Oren Idelman, 33, an investment adviser at a nearby bank, said, “I’m prepared to live like this for months, as long as the army continues this aggressive line.” The Gazans “have to understand that if we get hit, they get hit,” he said.

In Netivot, an Israeli town east of Gaza, clusters of people waited at bus stops with small suitcases when the Sabbath ended on Saturday evening, hours after a local man was killed in a rocket attack.

But nobody seemed to be speaking of leaving Ashdod, perhaps because of the shrinking number of places where it was safe to go.

“I’ve been here since 1976,” said Avraham Ohana, an older resident. “We are used to wars. But they always used to happen somewhere else, far away.”

As Mr. Ohana spoke, his brother called on his cellphone and urged him to come and stay with him in Haifa, about 80 miles to the north.

“I said, ‘What for? To be within range of Nasrallah’s rockets?’ ” he joked bleakly, referring to Sheik Hassan Nasrallah, the leader of Hezbollah, the militant Lebanese group that fired thousands of Katyusha-type rockets into northern Israel in 2006 when they fought a 34-day war.

http://www.nytimes.com/2008/12/31/world/middleeast/31israel.html?pagewanted=print

Copyright 2008 The New York Times Company