Afghan forces are participating in the offensive in Kandahar's Panjwayi and Zhari districts, where NATO's biggest ground battle in its history — Operation Medusa — was fought in September.
Brig. Richard E. Nugee, the chief spokesman for NATO's International Security Assistance Force, said about 50 Taliban fighters have been killed in the operation.
There have been no casualties among NATO troops, but a number of senior Taliban leaders been killed in airstrikes against Taliban command posts, he said.
"Taliban leaders are fleeing or being killed, and the Taliban soldiers don't know what to do," Nugee said. "Like any organization, if you take out the head, often the body doesn't know what to do."
He said so far the joint forces have cleared three villages of Taliban.
In the latest violence, NATO and Afghan troops arrested about 20 Taliban militants Tuesday night in Panjwayi, said Capt. Andre Salloum, the ISAF spokesman in southern Afghanistan.
The joint forces surrounded a large compound nearby where about 100 Taliban were located. After the Taliban returned fire on the forces, ISAF called in an airstrike that killed several fighters, Salloum said.