Taliban envoys meeting American officials have reportedly agreed to bar international terror groups from Afghanistaninfo-icon, 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 Pakistaninfo-icon, would now take direct charge of the negotiations in Dohainfo-icon.

Zalmay Khalilzad, Donald Trumpinfo-icon'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 Stateinfo-icon 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 USinfo-icon embassies and attack the Worldinfo-icon 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.

This week's meetings, which had been originally slated for only two days, have also been dominated by Taliban demands for a withdrawal of American forces and a US call for a ceasefire. The militants have publicly called for a complete pull out, but are understood to be open to a phased withdrawal. Americainfo-icon wants long term bases in the country however.

"When talks take a long time it means the discussion is in a sensitive and important stage, and the participants are getting close to a positive result," Sayed Ehsan Taheri of the Afghan High Peace Council told Reuters.

America has said any eventual peace talks should be "Afghan owned and Afghan led" but progress has been hampered by the Taliban's refusal to talk to President Ashraf Ghani's Afghan government, dismissing it as a puppet administration of the Americans.

" We're a long way from a fully fledged peace agreement. This is going to be a long road," said Graeme Smith a consultant for International Crisis Group.

Donald Trump's disillusion with America's longest warinfo-icon has given impetus to Washington's efforts to find a political settlement to the 17-year-long conflictinfo-icon.

Mr Khalilzad has met the Taliban at least four times in recent months, but the bloodshed has continued unabated. Afghan civilians and security forces are suffering record levels of casualties. An attack on an intelligence training base in Wardak that killed at least 36, and by some reports more than 100, underlined the Taliban military threat.

Rahimullah Yusufzai, an expert on the Taliban, said the overrun of this week's talks represented "unprecedented" progress.

"I have never seen anything like this before," he told AFP.

"This is the first serious effort. And it has continued since July... they have agreed to disagree and continued to meet. That's why it's unprecedented."