A deal between the two sides could pave the way for direct talks between the government of President Ashraf Ghanio despite the fact that the militants consider his administration illegitimate.
The US and the Taliban have resolved differences in peace talks over US troop withdrawal from Afghanistan, as well as over insurgent guarantees on cutting ties with other extremist groups, a Taliban official said Tuesday.
The development came during US-Taliban talks over the past two days in the Gulf Arab state of Qatar, where the Taliban maintain a political office.
The US side did not immediately confirm or provide details of what was resolved but the US envoy reported "excellent progress" in the talks.
The Taliban official spoke on condition of anonymity because he was not authorised to discuss details of the negotiations.
Technical teams from the two sides were continuing discussions on Tuesday in Doha.
US peace envoy Zalmay Khalilzad, who has been tasked with finding a peaceful resolution to the nearly 18-year war, America's longest conflict, has made intra-Afghan talks and a permanent cease-fire among his priorities in the negotiations.
Khalilizad, who later travelled to New Delhi, said in a Twitter post overnight that "we have made excellent progress" in the discussions.
My team & Taliban representatives will continue to discuss technical details as well as steps and mechanisms required for a succesful implementation of the four-part agreement we've been working toward since my appointment. Agreement on these details is essential.— U.S. Special Representative Zalmay Khalilzad (@US4AfghanPeace) August 5, 2019
However, the talks in Qatar have sidelined the government in Kabul.
The Taliban refuse to talk directly with government representatives, accusing President Ashraf Ghani's government of being a puppet of the US.
TRT World's Tanya Goudsouzian has more on the talks.
The Taliban have kept up a near-daily rate of deadly attacks, despite holding several rounds of peace talks with Khalilizad since his appointment as peace envoy almost a year ago. The Taliban now control roughly half of Afghanistan and are at their strongest since 2001, when the US-led invasion toppled their government that had harboured al Qaeda leader Osama bin Laden.
The US and the Taliban now appear to be closing in on an agreement under which US forces would withdraw in exchange for guarantees that Afghanistan would not become a haven for other terrorist groups.
Khalilzad has said he is hoping for a final agreement by September 1, which would allow the withdrawal of US and NATO troops. More than 20,000 US and NATO troops are in Afghanistan, including some 14,000 US forces.
The US and NATO formally concluded their combat mission in 2014, but the American and allied troops continue to train and build the Afghan military. Separately, US forces also assist the Afghan troops in airstrikes and raids on the Taliban and against Daesh's affiliate in Afghanistan.
President Donald Trump has often expressed his exasperation with America's continued involvement in Afghanistan and his desire to bring troops home.