The latest negotiations come as pressure builds for some sort of breakthrough in the gruelling Afghan conflict, with Washington jostling for a resolution.
According to a Taliban spokesperson, the group's top political leader Mullah Abdul Ghani Baradar met with US peace envoy Zalmay Khalilzad and the men discussed "key aspects for a peaceful resolution of the Afghan issue".
Khalilzad, who has stressed "there is no final agreement until everything is agreed", has previously outlined the basic framework for a deal.
The pact would see the US agree to pull its forces from Afghanistan in return for the Taliban vowing to stop groups using the country as a safe haven.
According to the Taliban, Baradar told Khalilzad it was vital those two key points "be finalised".
Khalilzad, a former US ambassador to Afghanistan, has spent several months shuttling between Asian capitals and Washington in a bid to build consensus for a deal.
On Sunday, the Afghan-born envoy said Washington was "a bit impatient" to end the war, given its $45 billion annual cost to the US taxpayer and the continued toll on US forces, some 2,400 of whom have been killed since the US-led invasion in response to the September 11, 2001 attacks.
US President Donald Trump provided additional momentum when in December he told advisors he wanted to pull about half of America's 14,000 troops from Afghanistan.
Despite several rounds of negotiations between the US and the Taliban, none of the talks thus far have included the Afghan government, which the Taliban views as a puppet regime.
An initial attempt for an "intra-Afghan dialogue" -- due to take place last month in Doha -- collapsed at the last minute amid bickering over the lengthy list of delegates Afghan President Ashraf Ghani wanted to send.
Khalilzad went to Moscow last week, where Russia and China voiced support for the US plan for a peace deal and stressed the need for intra-Afghan dialogue that would see all sides in Afghanistan at a negotiating table.
He tweeted on Wednesday he was in Doha and had met with the Indonesian foreign minister, who offered support for the talks.
Meanwhile violence across Afghanistan continues apace, and the Taliban last month announced the start of their annual spring offensive.
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