Some of the dozens of Taleban who attacked police in the central province of Ghazni were slain in a battle that lasted about an hour, provincial government spokesman Ismail Jahangir told AFP.
The Zana Khan district police chief was one of the policemen who died, he said. "A big number of Taleban have also been killed, but we don't know exactly how many," Jahangir said.
A spokesman for the Taleban movement, Zabihullah Mujahed, confirmed that fighters with his group had carried out the attack but claimed they had not suffered casualties.
The US military announced it had killed "several" militants elsewhere in Ghazni, a once quiet province that has seen a steep rise in Taleban activity in the past year.
The rebels were hit during an operation to capture a militant leader responsible for bomb attacks on troops, the force said.
The militant was captured, the force said in a statement, correcting an earlier release saying the operation was in Baghlan province in the north.
Jahangir said four men were killed in the strikes in the same area, and authorities were investigating claims they may have been civilians.
In Paktika province, which adjoins Ghazni, two men were killed when a waistcoat they were packing with bombs for use in a suicide attack exploded, the government said.
"Two mullahs (prayer leaders) were killed when a suicide vest they were building went off prematurely," said Zemarai Bashary, spokesman for the interior ministry, which handles police matters.
The pair was in a mosque near the border with Pakistan, he said.
Two other militants were killed when a mine they were trying to plant in a road went off in the southern province of Kandahar, said police commander Abdul Raziq.
Unrest linked to the insurgency has increased every year since the Taleban were forced out in a US-led invasion in late 2001 for harbouring Al-Qaeda.
This year, about 800 Afghan security force personnel and around 150 international troops have lost their lives in insurgency-linked unrest as have hundreds of civilians, according to various official estimates.
There are no official figures for the number of rebels killed.