The operation was launched after suspected Taliban fighters killed two Afghan soldiers on Tuesday and torched two vehicles belonging to a non-governmental organisation north of Kandahar city, said Khalid Pashtun, spokesman for Kandahar provincial governor Gul Agha.
"We sent 500 Afghan soldiers and then the conflict started, and is still going on," he said.
"In this recent operation we have killed four Taliban fighters and arrested six of them," he said, adding there had been no government or coalition casualties so far.
The operation started on Friday in the Tora Ghar district east of Sha Wali Khot, which is 10 km north of Kandahar.
A "limited number" of US-led ground forces and helicopters were supporting the operation, Pashtun said.
"In the Tora Ghar area some Taliban fighters are under siege and it's difficult for them to escape," he said, estimating around 100 rebels were in the area.
"We sent 500 Afghan soldiers and then the conflict started, and is still going on."
The six arrested men were being held at Kandahar police headquarters.
Sha Wali Khot was formerly home to some Taliban officials and remnants of the group continue to launch attacks in the area.
Up to four fighters were killed during a separate clash north of Kandahar on Thursday after they were fired on from US helicopter gunships.
In another incident late on Thursday US Special Forces came under attack from three fighters in the province's Spin Boldak border area. They escaped into Pakistan. There were no casualties on either side.
Also on Thursday, Afghan police killed one suspected Taliban fighter and arrested five others when a group of them attacked a village police post in southern Kandahar.
Kandahar was the former heartland of the Taliban and some 20 months after the fall of the government remnants of the militia and their al-Qaeda allies continue to launch regular attacks.
A US-led coalition force of some 12,500 troops is currently hunting Taliban and al-Qaeda fighters in the southern and eastern provinces bordering Pakistan.