Britain's The Guardian newspaper said the talks were attended by Mullah Abdull Manan Akhund, brother of Taliban founder and long-time leader Mullah Omar who died in 2013.
A senior American diplomat was also present in the Qatar meetings, the newspaper said citing a Taliban official.
The Taliban and the US government have so far not commented officially on the development.
The outcome of the September meeting was not clear but a Taliban source told the newspaper that it "went positively and was held in a trouble-free atmosphere".
A second dialogue was held this month despite intensified nationwide fighting between insurgents and US-backed Afghan troops.
The meetings come after Pakistan -- the Taliban's historic backers -- hosted several rounds of international talks over the last year to jumpstart peace negotiations, which yielded little progress.
The dialogue process ground to a complete halt when the US killed former Taliban leader Mullah Akhtar Mansour in a drone strike in May.
The insurgency has shown stubborn resilience under new Taliban leader Haibatullah Akhundzada, attacking northern Kunduz city for a second time and threatening the capital of the southern opium-rich province of Helmand.
Mohammad Masoom Stanekzai, Afghanistan's intelligence chief, and National Security Advisor Mohammad Hanif Atmar attended one of the Qatar meetings, local Tolo television said citing a presidential palace source.
"While the government is fighting the Taliban we are simultaneously trying to talk to them. The purpose of these meetings is to find ways to end the 15-year insurgency," he added.
The official did not say if a new round of discussions would happen, but hinted that the dialogue process could accelerate in the winter months, when fighting usually ebbs.
No Pakistani officials were present in the latest talks, sources said.
(This story has not been edited by Business Standard staff and is auto-generated from a syndicated feed.)