"Today the Islamic Emirate Negotiation team, led by respected Mullah Baradar Akhund, resumed the talks with the US negotiation team from where they were called off," Suhail Shaheen, the Taliban's spokesperson for their office in Qatar, said on Twitter on Saturday, Efe news reported.
"Talks were held about the signing of the agreement and other related issues and the talks will continue tomorrow as well," Shaheen said, referring to a draft agreement that was "completed" during the ninth round of talks between the two sides before Trump called off dialog in September.
Anas Haqqani, the son of the founder of the deadly Haqqani network insurgent group, who was released in November from an Afghan jail during a prisoner swap, took part in Saturday's talks, according to Shaheen.
Haqqani and two of other high-ranking Taliban members were released by the Afghan government with US mediation in exchange for two western professors as a trust building measure.
The move also aimed to pave the way for the resumption of the stalled talks as well as intra-Afghan talks between the Taliban and the government.
The Taliban has rejected the possibility of holding face to face talks with the government of President Ashraf Ghani, claiming it lacks power and serves as a puppet to the west.
US Envoy for Afghan Reconciliation, Zalmay Khalilzad, played an active role in the prisoner exchange and has been leading the US delegation in the talks for over a year.
Before flying to Qatar for the peace talks, Khalilzad held a series of meetings with Afghan leaders and politic, including Ghani.
Ghani and Khalilzad discussed a ceasefire and Taliban safe havens in Pakistan.
Although a ceasefire or at least a reduction in violence has been one of the top demands of the Afghan government in recent months, the Taliban has refused to agree to a cessation in hostilities, arguing a peace deal needed to be signed with the US first.
( With inputs from IANS )