15 former key members of the Taliban are willing to surrender to the Afghan authorities.
They are in Afghanistan and are holding indirect talks with representatives of the governor of Kandahar.
Khalid Pashtoon, an official spokesman, will not identify any of them.
When asked whether the group included former Cabinet ministers, he replied: "It is possible." He would not elaborate. He says the surrender "might take a week or two or three or four."
"Approximately 15 Taliban leaders are willing to surrender," he said.
He added he didn't know whether the Taliban members will be turned over to US forces in the area if they surrendered.
"They are just talking with us," he said. "We haven't reached that level yet."
Last week, former Taliban Foreign Minister Mullah Wakil Ahmed Muttawakil gave himself up, US officials say.
He is the highest-ranking Taliban official known to be in custody.