Israel will continue its military offensive in the Gaza Strip at its own pace until Palestinian militants release a captured Israeli soldier and halt their rocket attacks, Prime Minister Ehud Olmert told his cabinet on Sunday.

The operation in Gaza is a "war for which it is impossible to set a timetable," Mr. Olmert said, according to briefings provided by an Israeli official. "We will continue this battle with level-headedness and patience, while making use of the proper means," he is reported to have said. "We cannot sit and not respond to the Qassam rocket fire."

Mr. Olmert ruled out negotiations with Hamas, which leads the Palestinian government and whose military branch is holding Cpl. Gilad Shalit, who was abducted during a raid into Israel on June 25.

He said he had been prepared to release prisoners to Mahmoud Abbas, the president of the Palestinian Authority, before the two men met for a formal meeting, and Mr. Abbas confirmed that on Friday. But Mr. Olmert said Sunday, "We intended to release them to moderate elements, not terrorist elements." Releasing prisoners to Hamas in response to a kidnapping would further damage Palestinian moderates and reward extremism, Mr. Olmert said.

He repeated to the cabinet that Israel would not reoccupy Gaza but would act militarily there as it saw fit. "We will operate, enter and pull out as needed," the official quoted Mr. Olmert as saying.

Maj. Gen. Yoav Galant, commander of Israel's southern region, said late Saturday that Israel was ready for a long campaign, planning to shift the focus of operations from place to place. "We are prepared to continue the operation a month, two months and, if need be, even more," he told Channel 2 television. "The Palestinians will do their reckoning. They will count hundreds of dead terrorists, they will count the damaged infrastructure, the destroyed offices, the damaged factories."

On Sunday, the Palestinians counted more dead, even as they mourned and buried four people, including three from the same family, killed Saturday night in the Shijaia neighborhood, near the Karni commercial crossing, in an explosion at a house. The Palestinians blamed Israel.

But Israel said that its investigation showed that the explosion did not come from an airstrike, and that intelligence reports later showed that the deaths had been caused by a Palestinian anti-tank rocket.

Capt. Jacob Dallal, a spokesman for the military, said the Israeli Air Force, which tracks its missiles carefully, reported that its missile "hit the intended target," which was a nearby street where armed militants were walking with weapons. He said the army did not know what happened to those men, but "we hit the area we targeted, not the house."

An Israeli military official said intelligence information developed later, presumably from a source within Gaza, "clearly says that it was a Palestinian anti-tank missile." The military official insisted on not being identified and said he could not be more specific.

On Sunday, a Palestinian civilian was killed by an Israeli missile fired at a car carrying Hamas militants in the southern town of Rafah. The militants apparently escaped from the car, and a second missile hit nearby, wounding bystanders. The dead man was identified as Bilal Sliman Rabah, an 18-year-old supermarket clerk. Seven other Palestinians were wounded, with one in very serious condition, hospital authorities said.

Earlier Sunday, just after midnight, the air force struck a group of armed militants near the Karni commercial crossing, wounding three, members of the Palestinian security forces said.

Airstrikes also destroyed a major bridge in Beit Hanun, in northern Gaza, and an electricity transformer there, making it difficult to travel easily to the city and cutting electricity and some water supplies.

Palestinians continued to fire Qassam rockets into Israel despite the military operation. One resident of the nearby Israeli town of Sderot was moderately wounded Sunday morning from shrapnel wounds to the chest when a Qassam hit. A second rocket hit a house, and three people were treated for shock.

Three of the four Palestinians killed Saturday in the house explosion were members of the Hajaj family — Um Ayman Hajaj, 48; her son Muhammad, 21; and her daughter Rawan, 6. Four other family members were wounded.

The house is on the very edge of the Palestinian area closest to the Karni crossing into Israel.

Iman Hajaj, 23, one of Mrs. Hajaj's 14 children, said she was in the house's living room during the explosion, where some were watching an Egyptian soap opera. Those people were wounded, she said; those who died were in the garden drinking tea or cooking corn over a fire. "We had been nervous for two days with the movement of tanks and the shells," Ms. Hajaj said, sitting in a room of mourning women, all covered in black head scarves and long black robes, in a relative's house nearby.

"My brother Muhammad, who died, had just arrived a minute before to visit my married sister," Ms. Hajaj said, beginning to cry, then held out her hand, holding a curved piece of shrapnel. "More than 20 pieces like this we took from the body of my mother," she said.

As she spoke, young women who lined the banister of the stairway all began to chant in unison, "With our souls, with our blood, we sacrifice ourselves for our martyr!"

Um Hassan Hajaj, the aunt of the dead mother, spoke angrily about what she said was the responsibility of Israel and the United States for the deaths in her family. "Look at what your weapons are doing to us!" she yelled. As the television cameras came closer, she turned to them and shouted: "One day the Muslim countries will change everything, and there will be hard days for America! Injustice never lasts."

As the bodies of the dead were brought, wrapped in the flags of Islamic Jihad and Fatah, there was screaming and ululating and the cascading sounds of gunfire from the militants surging around the courtyard. The militants wore various forms of mufti, waving weapons and flags, including the green of Hamas. As the small body of Rawan was carried, tiny in the stretcher, her face exposed, the wailing swelled, and Um Fathi Hajaj, the girl's grandmother, collapsed in tears.

As he walked along the route of the funeral march, Abu Ahmed, the spokesman for the Islamic Jihad's military wing, quietly promised retribution. "We have 70 suicide bombers in a new brigade awaiting orders to strike Israel," he said.

Asked whether Islamic Jihad would respect a negotiated political document calling for Palestinian military activity to concentrate on Israel proper, he smiled wearily. "All of historic Palestine is ours, and we don't distinguish between 1948 or 1967," he said.

Mr. Abbas, back in Ramallah, ordered two representatives to discuss the crisis with Syria and with the exiled leader of Hamas's political bureau, Khaled Meshal.

On Friday, in a news conference, Mr. Abbas said he did not know of any splits in Hamas and dealt only with the elected Hamas prime minister, Ismail Haniya, who called in vain for a mutual cease-fire on Saturday, quickly rejected by Israel without Corporal Shalit's release.

The Israeli Army also announced after an investigation that the only Israeli soldier who has died in this nearly two-week Gaza operation was accidentally killed by Israeli fire.

Greg Myre contributed reporting from Jerusalem for this article.

Copyright 2006 The New York Times Company