KABUL—Insurgents in southern Afghanistan hanged an 8-year-old boy six days after they abducted him, the Afghan government said Sunday.

The boy’s captors had demanded that his father, a police officer, supply them with a police vehicle and he refused, said a statement from President Hamid Karzai’s office. The militants hanged the boy Friday in Helmand province’s Gereshk district.

“President Karzai both strongly condemns this act and rejects it as a brutal and cowardly crime that is not acceptable in any religion or culture,” the statement said. It referred to the killers as “terrorists,” but did not say if they belonged to the Taliban or another of the insurgent movements fighting foreign forces and their Afghan allies.

Kidnappings have become increasingly common in Afghanistan, both by criminal groups looking for ransoms and insurgents making a political statement. Most abductions are settled out of the public eye, with negotiations and cash payments.

Separately, Afghan officials said NATO forces battling insurgents along an eastern highway accidentally killed three civilians who were caught in the crossfire.

NATO said that local residents presented the bodies of three civilians killed. Spokesman Capt. Justin Brockhoff said it was unclear whose fire had killed them.

The battle broke out after international troops struck a roadside bomb in Wardak province.

The dead included a woman who was a provincial health official. Wardak government spokesman Shahidullah Shahid said Dr. Aqeela Hekmat and two of her family members were killed in their vehicle, and her husband was injured. Aqeela was the head of gynecology and maternal health for neighbouring Ghazni province.

Provincial police Chief Gen. Abdul Qayum Baqizai also confirmed three deaths and said it was clear that they were killed by NATO fire.

Karzai’s office said it was investigating the allegations.