Mullah Basir was shot in the head by police as he left a mosque in Char Diwar in Andar district, governor Mirajudin Patan told the BBC.
He said Basir had refused to surrender. Two other Taleban members with him were also arrested, the governor said.
Correspondents say Mullah Basir was key figure in the Taleban and had many men under his command.
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