Mullah Akhtar Mansoor was appointed as chief of Taliban after death of Mullah Omar. Agha had never been on good terms with Mansoor even during Mullah Omar's life.
Agha, who was a close confidant of Mullah Omar, said he would no longer represent the Taliban political office but would remain a member of the Taliban movement, The Express Tribune reported.
"I have decided to step down as head of the political office of the Islamic Emirate, because my political role has come to an end. I will not be part of any decision and statements of the Islamic Emirate Taliban," he said.
He opposed the appointment of Mullah Akhtar Mansoor saying that Taliban's new chief should have been elected among the Taliban fighters and in the bunkers.
Mullah Mansoor was chosen to replace Mullah Omar days after the death of the Taliban creator was officially confirmed by the Afghan Taliban on July 30.
He also expressed regret over the decision to keep news of Mullah Omar's death a secret.
The resignation comes at a time when splits among the Taliban are apparent over the election of Mullah Akhtar Mansoor as Mullah Omar's successor. Many top leaders and council members including Mullah Omar's son Mullah Abdul Qayyum Zakir are unhappy over appointment of Mullah Akhtar Mansoor.