The Taliban held its first direct contact with a US official in a preliminary discussion about future peace talks on Afghanistan, according to a senior official with the insurgent group.

It marked one of the most significant developments amid efforts to find a negotiated end to the country's protracted war.

The official described as "useful" a meeting with Alice Wells, the US's top diplomat for South Asia, earlier this week.

He said the meeting was held in the small Middle Eastern country of Qatar, where the Taliban have maintained a political office since 2013.

"The environment was positive and the discussion was useful," the Taliban official said on condition of anonymity because he was not authorised to speak to the media.

US officials neither confirmed nor denied a meeting took place.

However, Ms Wells was in Doha, the Qatar capital, this week.

While the US has not confirmed the talks, Ms Wells was in Doha this week. ( AP: Raad Adayleh )

In a statement following her return, the State Department said only that Ms Wells had been in Doha, had met with the ruling family and "the United States is exploring all avenues to advance a peace process in close consultation with the Afghan Government".

Any talks about a future political setup would be between the Taliban and the Afghan Government, the statement said.

The Taliban have long demanded direct talks with Washington, saying it does not want to talk politics with the US but instead meet face to face to discuss Washington's concerns — particularly its security concerns — about the Taliban and Taliban involvement in Afghanistan's future.

It also says it wants a time frame for the withdrawal of the roughly 15,000 US and NATO troops still in Afghanistan.

It wasn't clear when the next meeting would be held or with whom, but the Taliban official who spoke on condition of anonymity was certain one would be held.

Sorry, this video has expired Taliban fighters were embraced by civilians during a brief Eid ceasefire last month.

'Taliban want to solve problems with the Americans'

A former Taliban minister and ex-head of their political committee, Aga Jan Mohtism, who has maintained close contacts with the insurgent group, also confirmed a meeting in Doha between US officials and the Taliban took place earlier this week.

"The Taliban want to solve their problems with the Americans to end the invasion," he said.

The Taliban has argued that the Afghan Government cannot act independent of Washington.

It also said unless they can allay US concerns about the group, an agreement with Kabul would be meaningless.

Reports of peace talks came as suicide bomb attacks continued to rock Afghanistan.

At least three people were killed after a bomber detonated his explosives vest, paving the way for another attacker to charge into a training centre for midwives in the capital of Nangarhar province, a provincial official said on Saturday.

No one immediately claimed responsibility for the attack, but both Taliban insurgents and fighters from the local affiliate of the Islamic State group are active in eastern Afghanistan, especially in Nangarhar.

A previous attempt at direct talks between Washington and the Taliban in 2013 also in Doha, was scuttled when then-Afghan President Hamid Karzai objected to the Taliban calling its office the Islamic Emirate of Afghanistan — the name of its government — and flying the flag the movement flew when they ruled Afghanistan.

At the time the direct talks, which the Taliban also said would be restricted to US concerns about the movement and troop withdrawal, was to be followed by talks between the Taliban and the Afghan Government.

There was also a suggestion at the time that the talks would include the freedom of five Taliban prisoners held in the US prison at Guantanamo Bay and the release of captured US soldier Bowe Bergdahl.

His release was eventually secured in May 2014 in exchange for the five Taliban prisoners, who are living in Doha.

AP