Hundreds of troops were sent into Arghandab
Nato and Afghan forces say they have driven Taleban fighters from areas close to the southern city of Kandahar.
A Nato spokesman said troops had met little resistance in Arghandab district near the city and there had been only sporadic clashes.
Afghan officials say 56 Taleban and two Afghan troops died in the fighting, but there is no independent confirmation.
Hundreds of people fled their homes in the Arghandab area before the operation which involved more than 2,000 troops.
The operation began on Wednesday after the Taleban said they had taken charge of large parts of the district near the provincial capital.
At a joint press conference, a Nato spokesman said troops were now firmly in control of the area.
"So far our assessment is that if the insurgents are there they have not the numbers and the foothold that they previously claimed," spokesman Gen Carlos Branco said, the AFP news agency reports.
"Obviously, they did choose not to fight."
A number of Taleban fighters had been killed in airstrikes, he said.
Earlier Kandahar Governor Assadullah Khalid said the Taleban had "suffered hundreds of dead and wounded and many of their casualties are Pakistanis".
The BBC's Martin Patience in Kabul says the operation is being hailed a success by the Afghan government which has come under immense pressure to reassert its control in the province.
There has been a build up of Nato and Afghan forces in Arghandab district
Last week, the Taleban staged a massive jailbreak from Kandahar jail, freeing at least 350 insurgents.
The attack was hailed as a major triumph for the Taleban, which draws much of its support from the south of the country.
It is not clear whether some of those militants who escaped were being targeted in the operation, which Nato says is still continuing.
The Afghan defence ministry had estimated that around 300 to 400 militant fighters were operating in Arghandab district and had taken at least eight villages.
Arghandab district lies about 5km (three miles) north of Kandahar and is an important agricultural area.
It offers good fighting positions for Taleban militants with its vineyards and pomegranate orchards and numerous irrigation ditches.
Kandahar is one of the key battlegrounds of the current rebel insurgency against Afghanistan's government and troops from Nato and a US-led coalition.
President Hamid Karzai is from the city and it is also the birthplace of the Taleban.