“He said, ‘Well, one brother you’re going to have.’ ”

The officer told her brother to sit on the floor against a wall between a bedroom and the kitchen, she said. Then he fired four or five shots from a rifle into Mr. Spence’s chest and head. As officers dragged Mr. Spence’s body out by his feet, another police officer, a woman, was directed to pick up the shells, the witnesses said.

The episode is among several accusations of extrajudicial killings during several days of fighting that left at least 70 civilians and 3 members of the security forces dead, as state security forces made an assault on the garrison neighborhood of Tivoli Gardens to arrest a crime leader named Christopher Coke, who remains at large. Officials later said they met fierce resistance from gunmen, and during the battle, soldiers and police officers searched for men of fighting age, convinced that supporters of Mr. Coke from other neighborhoods had joined the fight.

Witnesses assert that the police simply executed some of them based not on evidence but on age.

The account of Mr. Spence’s killing was based on interviews with four people who said they saw the shooting: two female neighbors, Mr. Spence’s sister and his girlfriend. They said Mr. Spence was unarmed.

A police spokesman, Gilmore Hinds, declined to comment on the specifics of the accusations, pending at least two state investigations, but he called the story “incredible.”

Though their stories could not be verified, several other people within a few blocks of Tivoli Gardens also say that young men in their families, not gunmen, were killed by police officers or soldiers. Mr. Hinds said combatants were among those the security forces had killed, but the government has provided little evidence — a photograph of a dead man with a gun, for example, or the biography of a dead fighter.

As relatives search for answers about the killings, questions are emerging about the capacity of Jamaica’s public defender, Earl Witter, whose office is badly underfinanced, to investigate all of the accusations fully and swiftly. The police said they were also investigating the killings.

Mr. Witter said that he had reached out to the United Nations Development Agency and the United States Agency for International Development for help finding forensic pathologists and radiologists overseas who could help with the autopsies, which have been delayed. Mr. Witter said he also needed help from independent firearms examiners to analyze bullet fragments.

Mr. Witter confirmed that he had visited the apartment where Mr. Spence’s relatives said he was killed, but declined to comment on the case.

Several of the accusations emerging from Tivoli Gardens center on the conduct of officers in the Jamaica Constabulary Force, which has faced criticism in the past by human rights groups like Amnesty International for the relatively high number of people killed by police officers every year. In recent years, Amnesty found, 12 percent of killings were committed by police officers. At the same time, in a country with one of the world’s highest rates of violent crime, much of it stemming from intractable gang violence, 12 to 14 police officers are killed every year, according to the department.

Mr. Hinds, the police spokesman, called inquiries into reports of brutality “premature” and emphasized that accounts of civilian casualties should be measured in context.

“All the entrances were barricaded, and those barricades had detonators placed in them,” he said. “There were snipers on the buildings.”

He added: “I’m certain the majority of the people who were killed were adult males — able-bodied adult males. Only two were women. The majority of them were killed at the barricaded entrances, in the gullies or in front of buildings. And I’m certain an investigation would reveal that some of them would have weapons on them.”

The fighting, which began on May 24, was intense. The police have released photographs and video that appear to show gunmen in an area that looks like Tivoli Gardens. The men peer from behind sandbags on balconies and walk around with guns.

Much damage is concentrated at one end of Wilton Hill Drive, a street of single-family homes where an explosion apparently injured residents and shattered windows.

An explosion does not seem to explain what happened at No. 11, a two-story house where Jane McFarlane believes her 25-year-old-son, Martin Lindsay, and a cousin, Oshane Walker 19, were killed by police officers.

The killings occurred on May 26, near the offensive’s end and as the streets of Tivoli Gardens were quieting down, she said.

“Everything was going smooth,” said Ms. McFarlane, who was not at home at the time. Shortly before 2 p.m., she said, Mr. Walker called her cellphone, saying he had been shot in the back.

“He said, ‘Martin dead,’ and he hung up the phone,” she said. “I call back the number. He said, ‘Martin dead — they shot him in the chest and me got shot in my back.’ ” Mr. Walker told her he was upstairs.

Ms. McFarlane said she asked him who was shooting, and he answered that it was the police. Then the line went dead.

She said people on the block told her three bodies were pulled out of the house, which is still filled with blood: in the living room, in the kitchen, in a trail leading to a bedroom upstairs, where the blood is thick and spattered against all the furniture.

Ms. McFarlane said neither of the men were fighters, or associated with Mr. Coke. “Better that they associate with him,” she said. “Then I could say at least I know why they got them.”

Mr. Spence’s friends and relatives, replaying the events that day, also struggled to explain why he was dead.

After finding Mr. Spence to be unarmed, an officer asked for proof that he belonged there. His mother and his sister showed a family photo album.

The order to kill Mr. Spence, they said, was given by another officer, who silently drew his finger across his neck. Ms. Spence said they were told that because of the “state of emergency,” police officers had permission from their superiors to kill men Mr. Spence’s age.

She said they were told not to cry, or to make a sound, or they would be killed, too.