Taliban envoys meeting American officials have reportedly agreed to bar international terror groups from Afghanistan, in a significant concession to Washington's fears the country will again become a terrorist haven.

Talks between the adversaries on Thursday reached the end of their fourth day, raising hopes the lengthy session would bring more progress.

Taliban sources also said Mullah Abdul Ghani Baradar, the militants' former number two who was recently released from custody in Pakistan, would now take direct charge of the negotiations in Doha.

Zalmay Khalilzad, Donald Trump's peace envoy to the country, was understood to be pushing for an initial agreement that would pave the way to bring the Afghan government into talks.

American negotiators have sought assurances that after any peace deal, jihadist militants such as al Qaeda and the Islamic State group would not be allowed to plot attacks against the West.

Osama bin Laden spent much of the 1990s in Afghanistan as a guest of the Taliban and was living on a farm outside Kandahar as al Qaeda hatched plans to bomb US embassies and attack the World Trade Centre.

The Taliban have now agreed to the assurances, the Wall Street Journal reported, despite concerns by some militant officials that rank-and-file fighters would view the move as joining forces with Washington against al Qaeda.