A police officer who arrived after the shooting said that Mr. Shukrullah, who was a graduate of the police academy, was at the house that night only by chance.

“He was supposed to be on patrol with others, but someone else went on patrol instead of him because he was still new and didn’t know the villages very well,” said the officer, who asked that his name not be used because he was not supposed to speak to reporters.

“He was a really good officer,” his colleague said, adding, “He was shot twice: once in the head and once in the chest. His pistol magazine was full. No round had been fired from it.”

The NATO statement said Mr. Shukrullah was shot because he was armed and had threatened the troops. “One man then threatened the security force with a pistol; the security force defended themselves, killing the man.”

Rear Adm. Harold Pittman, NATO’s deputy chief of staff for communications, apologized for the deaths. “We are deeply sorry for this tragedy and apologize to the members of the Afghan government, the people of Afghanistan and most importantly, the surviving family members of those killed by our actions,” Admiral Pittman said. “We understand any civilian loss of life is detrimental to our cause and to our efforts to secure the population.”

For Mr. Mohammed, the words were little comfort. “They killed my 12 year-old innocent daughter and my brother-in-law and then told me, ‘We are sorry,’ ” he said. “What does it mean? What pain can be cured by this word ‘sorry’ ?”