The violence began on Wednesday when Taliban fighters attacked a police checkpoint in Uruzgan province's Tirin Kot district and an ensuing hour-long gunbattle left seven attackers dead, said provincial governor Jan Mohammed Khan on Friday.
Then on Thursday, the fighters assaulted Saiban, a nearby village, and kidnapped nine tribal elders and a 10-year-old boy, he said.
All nine were later executed and the boy was sent to the authorities with a message: If the police hand over the bodies of the seven slain fighters, the captors will release the bodies of the nine, he told The Associated Press.
The police did not respond to the offer.
Then on Friday, fighters attacked another police post nearby and four officers and five of the attackers were killed, Khan said.
He said the government has ordered its security forces to hunt down the fighters.
The killings follow three months of unprecedented fighting that has killed about 477 suspected fighters, 47 Afghan police and soldiers, 134 civilians, and 45 US troops, including 16 troops killed in a helicopter crash earlier this week.