KIRYAT SHEMONA, Israel — The Biton family had reached their breaking point. After a month confined to a stuffy, dusty, underground bunker, this family from the northern Israeli town of Kiryat Shemona decided to risk emerging for fresh air.

“We cannot go on living like this,” a 29-year-old jewelry shop assistant with two infant girls, Yael Biton, said. But unlike hundreds of others who yesterday joined the first stage evacuation organized by the government, the family is staying put.

Mrs. Biton grabbed a mop and began frantically cleaning her family’s ground floor flat. It was the first time that she had cleaned since Israel’s war with Hezbollah began four weeks ago. Since then, her hometown has received 700 rocket hits by the Lebanese Shiite militia, more than any city in Israel.

“I am sorry for the state of our home, but we have not really been living here properly for weeks,” she said. “We have spent days down there, nights down there. It is driving us crazy.”

“Down there” is a bleak subterranean chamber illuminated by strip lighting and reached by descending 19 steps. “It’s the children that suffer the most,” she said, as she showed me around the humid, oven-hot bunker.

“At the beginning of the war, there were as many as 20 people down there with lots of children, and … one child would always want to play while others were trying to sleep. It was chaos.”

The floor of the bunker was covered with toys belonging to the two Biton girls, Zoel, 4, and Ellia, 18 months. Next to a smiling face drawn on the wall with a crayon, Mrs. Biton had written “2006 — War Of No Other Choice.”

When the war began, the Bitons and their neighbors in the Itzhak Sade suburb of the town dutifully descended to the shelter whenever the sirens sounded.

But after a few days, tempers began to fray, and various people left, heading south to stay with relatives in parts of Israel beyond the range of the Hezbollah rockets.

Mr. and Mrs. Biton have no relatives who live in safe parts of Israel, so they spent their savings on a few nights of hotel accommodation down south. When the money ran out, they returned to the shelter.

“I was born in Kiryat Shemona, and I have lived through Palestinian rockets in the 1980s and Hezbollah rockets in the 1990s,” Gavriel Biton, 41, said.

“But I really did not want my children to have to live through the same thing and cope with the same pressure.” On Tuesday, across town in another underground bunker housing the command center of Mayor Haim Berbibai, council workers were organizing the first buses paid for by the Israeli government to move locals to safety.

It was bedlam. Workers with lists of people and telephone numbers ran around a web of temporary telephone lines trying to come up with an accurate list of those who wanted to go and places that would be willing to take them. Residents who had not been included on the list forced their way in to shout at the mayor and his staff.

“You are only moving your families and friends. What about us, the real people who have been shelled for a month? You’ve done nothing for us,” Ziv Benitach, 31, screamed.

Described as “rest and recuperation” trips, the government insisted that the people would spend only a few days down south before returning to Kiryat Shemona.

To say anything else would suggest that it is not winning the war against Hezbollah.

Back at the Biton household, no one spoke of leaving. From only a few miles out of town, in the upper Jordan valley, Israeli howitzers fired a rolling thunder of shells into Lebanon, and Zoel carried on playing.

The Bitons’ brief respite lasted only an hour or two before the sirens started wailing again at 5 p.m., and the family descended the 19 steps again to wait out the latest barrage.