“We have repeatedly warned the A.L.P. recruiters and trainers to conduct proper and accurate vetting processes for people who want to join the A.L.P. ranks,” said Fiazanullah Fiazan, a former provincial governor in Ghazni. “We have told them not to enroll unknown people or people who are not vouched by tribal elders, but they don’t listen. They are trying to meet the recruiting deadline and get credit for it.”

A spokesman for the Special Operations troops in Afghanistan could not be reached for comment. A spokesman for the NATO-led International Security Assistance Force referred all questions to Afghan officials.

A spokesman for the Taliban, Zabiullah Mujahid, e-mailed a statement to journalists claiming Taliban responsibility for the attack.

“Locals in the area were tired of the atrocities and crimes of these arbakais, and their lives and property were not safe,” Mr. Mujahid wrote, using the Afghan term for irregular militias. The deaths of the police officers, he said, meant that “oppression has been weakened and decreased in the area.”

In the episode in Kandahar Province, the authorities said, three National Police officers were found shot to death outside their post on the outskirts of Kandahar. A spokesman for the police, Ghorzang, who like many Afghans goes by only one name, said the attacker was not an insurgent, but a heroin addict and a relative of the post commander, who was one of the victims.

Mr. Ghorzang said that the commander had taken the relative to get treatment and that after the police in the post fell asleep the relative took one of their guns and killed the commander and two other officers. The attacker, who was not identified by name, escaped.

But a spokesman for the Taliban in southern Afghanistan, Qari Yousuf Ahmadi, reached by telephone, said the insurgents had recruited the assailant and took responsibility for the attack.