The capture of the head of Mulla Umar's household security on Tuesday could help US and Afghan forces track down his boss, one of the most wanted fugitives in the US-led "war on terror".
"We have arrested top Taliban figures Toor Mulla Naqibullah Khan and Mulla Angar on the way between Arghandab and Kandahar," said a Kandahar official.
"They were carrying a satellite telephone and some important documents.
"We are hopeful we will arrest more Taliban figures and we hope that we can arrest their leader Mulla Umar," he said.
Khalid Pashtun, a spokesman for the provincial government, confirmed the arrests.
Mulla Umar's Taliban militias have been waging an insurgency in the south and southeast of Afghanistan since they were driven from power in late 2001 by US and Afghan forces.
Toor Mulla Naqibullah Khan was unarmed when he was arrested with Mulla Angar, another Taliban commander, on Monday evening. The security official said they were picked up following a tip from a Taliban insider.
There are about 18,000 US-led
troops in Afghanistan
President Hamid Karzai offered to let any Taliban fighters resume a peaceful life after he was elected in the country's first presidential vote on 9 October.
Some Taliban figures will be shown no clemency because of the alleged gravity of their crimes against the nation, however. The government, with input from US authorities, is expected to draw up a list of fighters who will not be accepted back into the mainstream.
US-led forces launched a winter offensive called Operation Lightning Freedom last week, aimed a preventing the Taliban from regrouping to pose a threat to parliamentary elections expected in April.