Taliban officials secretly met a senior US diplomat in Qatar last week, sources in the group have told the BBC.
The face-to-face talks in Doha with Alice Wells, a state department deputy assistant secretary, were "very important", one Taliban official said.
News of the meeting follows a directive from the Trump administration for US diplomats to talk directly with the Afghan militant group.
The Taliban have long said that only with the US will they discuss peace.
Direct talks with the militants, without Afghan officials present, marks a major turnaround in Washington's policy as it seeks to end America's longest war.
It comes after an unprecedented three-day ceasefire during Eid celebrations in June that was largely respected by both sides. There have been attacks since, including one on army check points in Badghis province.
The meeting was first reported by the Wall Street Journal. Two senior Taliban sources confirmed it to the BBC's Mahfouz Zubaide, in Kabul. They said a six-member delegation was led by Abbas Stanikzai, who heads the group's political office in Doha.
The US department of state has confirmed that Ms Wells, of the Bureau of South and Central Asian Affairs, was in Qatar last week to meet government officials and talk about an Afghan peace process but did not confirm or deny the Taliban meeting.
One of the Taliban officials described the talks as a "preliminary" discussion to set up a channel between the group and senior US officials ahead of further meetings. Neither would provide further details.
Another official told Reuters news agency: "We agreed to meet again soon and resolve the Afghan conflict through dialogue".
There are reports that two other meetings have taken place but this could not be confirmed.
The Taliban are reported to have insisted that no Afghan officials should be present at the meeting with Ms Wells. The US has previously insisted that Afghan officials must be part of peace talks.
The US invaded Afghanistan in 2001 in the wake of the 11 September attacks, ousting the Taliban from power and setting the stage for what has turned into a 17-year conflict.
President Donald Trump re-committed the US to the war in a new strategy last year, and stepped up air strikes against the militants to try to force them to the negotiating table.
A previous attempt at direct talks in Doha failed in 2013, when then Afghan President Hamid Karzai became angry that the Taliban were flying a flag outside their new Qatar office and using the name of the Islamic state they founded when they came to power in the 1990s - the Islamic Emirate of Afghanistan.