Taliban commander Mullah Rahim said the 13 were captured in a raid on Mian Nishin district in the southern region of Kandahar on Thursday.
"We have hidden them somewhere and will decide on their fate following instructions from our leadership," Rahim told Reuters, using a satellite phone belonging to the district police chief.
A senior police officer in Kandahar city confirmed that the phone belonged to the police chief and that authorities had lost touch with the 13.
Mian Nishin was the scene of joint operations by Afghan and U.S.-led forces this week in which government officials said nine guerrillas were killed.
Recent weeks have seen a surge in Taliban-linked violence in the south and east of Afghanistan, raising feares for the security of parliamentary elections due to be held on Sept. 18.
In another incident on Thursday, three guerrillas were killed while trying to ambush a government convoy in neighbouring Zabul province, provincial spokesman Gulab Shah said.
A Taliban spokesman denied the report and said the Taliban had inflicted losses on the government forces in the ambush.
Kandahar has been the scene of much of the recent violence.
On Monday, four U.S. soldiers were wounded in a suicide attack outside Kandahar city, where at least 20 people lost their lives in a suicide bomb attack on a mosque on June 1.
The Taliban have threatened more violence, and both President Hamid Karzai and U.S. ambassador Zalmay Khalilzad have warned the guerrillas are likely to step up attacks ahead of the elections.
More than 150 insurgents have been killed this year, according to U.S. and government figures. Dozens of government troops and 13 U.S. soldiers from the 20,000-strong U.S-led foreign force hunting the militants have also died since March.
U.S.-led forces overthrew the Taliban in late 2001 after they refused to hand over al Qaeda chief Osama bin Laden, the architect of Sept. 11 attacks on the United States.
On Thursday, Khalilzad said he did not believe bin Laden or Taliban leader Mullah Mohammad Omar were in Afghanistan. He was responding to comments by a senior Taliban commander the previous day who said bin Laden was in good health and that Omar was in direct command of Taliban forces in Afghanistan.
- Reuters - Thomson Reuters Foundation
- For more humanitarian news and analysis, please visit https://www.trust.org/alertnet