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Sources told The Guardian that among those present at the meetings held in September and October was Mullah Abdul Manan Akhund, the brother of Mullah Omar, the former Taliban chief who led the movement from its earliest days until his death in 2013.
The two rounds of talks are the first known negotiations to have taken place since a Pakistan-brokered process entirely broke down following the death of Omar's successor Mullah Akhtar Mansoor in a US drone strike.
The presence of the US officials helped make the meeting possible given the Taliban's long standing reluctance to meet directly with the Afghan Government, which it publicly lambasts as a "puppet regime".
The US embassy in Afghanistan declined to comment on the claim.
The Taliban official said the first meeting in early September "went positively and was held in a trouble-free atmosphere" in which Akhund sat face to face with Mohammed Masoom Stanekzai, Afghanistan's intelligence chief.
A second meeting took place in early October despite continued fighting between the government and insurgent forces.
Recent weeks have seen the Taliban overrun Kunduz for the second time and threaten Lashkar Gah in Helmand.
Although an Afghan Government official confirmed Stanekzai had made at least one recent trip to Doha, both Ashraf Ghani's spokesman and Ismail Qasemiyar, a senior member of the High Peace Council charged with overseeing peace talks, denied any knowledge of the meetings.
The last known meeting between the two sides took place in the Pakistani hill resort of Murree in July 2015 where the US and Pakistani officials were also present.
But Pakistan has been unable to orchestrate any further meetings following the death of Mansoor.