Afghan forces backed by their US and Canadian allies are claiming to have surrounded 250 Taliban fighters in the southern district of Arghandab outside Kandahar.
Three days of fierce fighting in the region have also left 50 Taliban fighters dead, the Afghan security sources have said.
"Since yesterday there has not been any direct fighting in Arghandab district," Sayed Aqa Saqib, the provincial police chief, said.
"We are carrying out our clean-up operations. We have not faced any resistance so far."
But Al Jazeera's Hamish Macdonald reporting from Afghanistan said that the fighting was not over yet and that the Taliban fighters are seeking to get reinforcements.
An Afghan man told Macdonald that his son has been asked by the Taliban to join the fight.
Separately, Afghan forces say they have killed 50 Taliban fighters in the heaviest fighting in a western province of Afghanistan.
Mohammad Gul Sarjang, the provincial police spokesman, said on Thursday that the clashes in the troubled Farah province was continuing for a third day.
"The fighting is still ongoing in Gulistan district. We killed 20 more Taliban since yesterday," Sarjang said. "Five soldiers and seven police have also been killed so far."
On Wednesday Afghan police said up to 40 Taliban fighters were killed and 20 wounded.
The Taliban dispute the casualty figures and maintain they are in control of the district.
Taliban fighters also attacked another district of Farah on Wednesday night, sparking a six-hour fight with security forces, Sarjang said.
Civilians killed
US-led coalition forces meanwhile have killed two children and a 75-year-old man in a raid on a house in eastern Afghanistan.
The deaths occurred in Batti Kot district of Nangarhar province late on Wednesday, the Afghan police said on Thursday.
"They have killed a 75-year old man, a 16-year-old girl and a young boy in the firefight", said a local police chief.
Two other civilians were treated for injuries and three people were arrested by coalition forces.
A coalition statement said its forces killed a fighter after suspecting the house to be a hideout for facilitators of suicide bombings and improvised explosive attacks.
"It wasn't until after the hostilities had stopped and the team had performed a search of the room that they found two children dead. A wounded adult female and child were also found", it said