Taliban and Afghanistan secretly 'restart peace talks' in Qatar
The talks were held in the presence of a senior US diplomat and attended by Mullah Abdul Manan, the brother of Taliban chief Mullah Mohammed Omar who died in 2013.
The first session of peace talks took place in September and was followed by another in October, according to the Guardian.
The presence of a US official made the meetings possible, a source told the newspaper.
"Taliban believes the Afghan issue is a dispute with both the US and Afghan governments," the source said. "If these three sides can hold preliminary meetings it could create a strong base for further positive developments."
Previous Pakistan-brokered peace talks failed after a US drone strike in Pakistan killed former Taliban leader Mullah Akhtar Mansour in May.
Fighting raged across Afghanistan this year, with the militant group attacking the northern city of Kunduz and threatening the southern Helmand's provincial capital Lashkar Gah.
In August, the US - which backs Kabul with air power and other military support - rushed over a hundred troops to Lashkar Gah to prevent Afghani Taliban overrunning the city.
Earlier this month, Taliban militants launched a full-fledged attack on Kunduz, briefly entering the northern city and triggering fierce fighting with Afghan forces, forcing thousands of civilians to flee.
The total number of internally displaced people due to fighting since the start of the year stands at 323,500.