An official in the National Unity Government in Kabul told AFP that the two rounds of discussions took place in Doha, where the Taliban maintain a political office.
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.
Afghan Forces fail to retake Kunduz from Afghan Taliban clutches
Over the last year, Pakistan -- the Taliban 's historic backers -- have hosted several rounds of international talks 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.
Afghan Taliban receive peace talks invitation from Afghanistan Government
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.
Afghan Taliban to hold direct talks with USA through Doha Political Office
"In Afghanistan war and peace go hand in hand," another Afghan official told AFP, confirming the Qatar meetings.
"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.