The insurgent group's meeting with Alice Wells, America's top diplomat for South Asia, was a bid to kick-start talks on ending the 17-year conflict, an unnamed senior Taliban official said.
US officials neither confirmed nor denied a meeting took place, but noted Ms Wells had been in the Qatari capital Doha this week, where she met with government officials "to discuss recent progress towards an Afghan-owned, and Afghan-led peace process".
They added that Washington was "exploring all avenues to advance a peace process in close consultation with the Afghan government".
The Taliban, which has a political office in Qatar that serves as an unofficial embassy, has long demanded direct talks with the US.
"The discussion was preliminary, initial and both discussed a future meeting and contacts," said the Taliban official.
It is not clear when the next meeting would be held, but they were certain there would be one.