The Taliban official, on condition of anonymity, said that the meeting was held with Washington's top diplomat for South Asia, Alice Wells, earlier in the week in Qatar.
"The environment was positive and the discussion was useful," said the Taliban official on Sunday.
“You can’t call it peace talks...These are a series of meetings for initiating formal and purposeful talks. We agreed to meet again soon and resolve the Afghan conflict through dialogue,” he added, Press TV reported.
A former Taliban minister also confirmed that a meeting between US officials and the Taliban took place earlier this week in Doha.
"US officials and the Taliban took place earlier this week," said Aga Jan Mohtism.
The US has neither confirmed nor denied the meeting. However, Wells was officially in Doha last week.
"The United States is exploring all avenues to advance a peace process in close consultation with the Afghan government," said a statement released by the US State Department after her return.
Earlier in the month, the United States expressed readiness to initiate direct talks with the Taliban in an attempt to end a 17-year-old war in Afghanistan, a significant shift in American policy in the conflict-ridden country.