During his interrogation, Mr. Khan suggested that other weapons were involved in the battle for influence, as well. According to four officials familiar with the questioning, the Haqqani leader told his interrogators that the Taliban had been approaching Afghan government and military officials throughout the summer, persuading them to sign a five-page document secretly pledging their loyalty to the Taliban leadership. Mr. Khan boasted that he had signed up 20 officials himself.

“They tell the officials that the Taliban is going to be back in power within 20 days of NATO leaving, so if they want to live, they’ll sign,” said one of the American officials, who spoke on the condition of anonymity to discuss the classified interrogations. Officials say they have found no confirmation of such oaths, however.

In places like Sabari, a rural district in Khost that sits about a dozen miles from the Pakistan border, the targeted killings are producing their intended effect. After a daylight execution of three men in a bazaar in the village of Maktab about four months ago, shop owners were so traumatized that they never reported the killings to the authorities.

Often, the victims may have had little more than passing encounters with coalition forces, or no involvement at all, according to officials, witnesses, and friends and relatives of victims.

American and Afghan officials learned about the killings only later when a video of the episode was found on a captured insurgent’s cellphone. Even then, American officials who showed the video to a New York Times reporter could cite the place where the killings had taken place but believed that they had occurred in October, about three months after witnesses say the actual episode happened.

The video showed a number of gunmen shooting to death two men as shop owners scrambled for cover. The militants then shot a third man as he sat in a white plastic chair in front of his shop. As the man fell backward, one of the gunmen shot him 10 more times in the face and chest.

“Whoever tries to help the Americans and spies for them will face this,” one of the men shouted after the killings, according to a witness, Ahmadullah, 25, a shop owner who like many Afghans goes by one name.