He said "NATO aircraft have started carrying out combat missions in the district," adding that 20 Taliban guerrillas and two Afghan army officers had been killed in the operation so far.
The Arghandab administration head, Mohammad Farooq, earlier said about 500 militants had seized several villages in the district forcing residents to flee their homes.
And the head of the Kandahar province council, Ahmed Wali Karzai said that 1,500 families had left the region to avoid NATO air strikes and being caught up in the fighting.
Hundreds of Taliban fighters swooped on the Arghandab district three days after the Islamist group, ousted from power after the U.S.-led military operation in 2001, mounted a daring attack on Kandahar's prison, freeing some 1,100 prisoners, including over 350 Taliban militants.
The offensive comes as four British troops, including the country's first female soldier, were killed Tuesday in a roadside bomb in the Helmand province.
With five members of the Parachute Regiment dying last week in the country the latest deaths bring the number of U.K. troops killed in Afghanistan up to 106.
NATO runs the 52,000-strong International Security and Assistance Forces (ISAF) in the country.