General Saif Allah, who led Afghan troops in the Daychopan battle, said Afghan soldiers had also arrested a top Taliban commander, Mullah Abd al-Salaam, in Naw Bahar.Abd al-Salaam, who was wounded, had apparently fled from Daychopan, he said.
Saif Allah said they were trying to block possible escape routes to Pakistan, where many of the Taliban rebels were thought to be based.
"We have American troops, their helicopters and other planes chasing the Taliban with us in Mizan, Naw Bahar and in areas close to Pakistan where they are likely to escape," he told Reuters.
He added that US warplanes killed nearly two dozen Taliban fighters in Naw Bahar on Wednesday, but said that there had not been any major engagements since then.
The US military said 84 to 95 “anti-coalition” forces had been killed, but Taliban commanders say their losses have been much lower while they have killed 50 Afghan government troops.
The expansion of the operation in the south, the Taliban's former bastion, coincides with a visit to Afghanistan of US Defense Secretary Donald Rumsfeld, who is expected on Sunday.
In May, Rumsfeld said most of Afghanistan was secure, and the United States had moved from a period of major combat operations to one of stabilisation and reconstruction.
Since then, Taliban forces and allied rebels have staged almost daily attacks on government posts, aid workers and US-led forces.
More than 220 people have been killed since 7 August, making the month the bloodiest since US-led forces overthrew the Taliban in late 2001.