The insurgents have been meeting with the US envoy in Doha to hammer out a deal that would see the US military quit Afghanistan in return for various guarantees.

"These six days have been the most productive of the rounds we've had with the Talibs," Khalilzad said in Qatar.

"Essentially the four items we have been talking about ever since we started (are) terrorism, withdrawal of foreign troops, inter-Afghan negotiations and dialogue, and ceasefire.

"For the first time I can say we have had substantive discussions, negotiations, and progress on all four issues."

The envoy added that direct US-Taliban talks seeking to end nearly 18 years of war would pause for a separate two-day meeting of Afghan representatives and resume on Tuesday.

Suhail Shaheen, the spokesman for the Taliban's office in Qatar, said they were pleased with the US discussions so far.

"We are happy with progress and hope the rest of the work is also done. We have not faced any obstacles yet," he tweeted.

- Intra-Afghan talks -

About 60 Afghan delegates are expected to attend the so-called intra-Afghan dialogue on Sunday and Monday, including political figures, women and various Afghan stakeholders.

The Taliban, who have steadfastly refused to negotiate with the government of President Ashraf Ghani, have stressed that those attending the intra-Afghan talks will only do so in a "personal capacity".

The United States will not be represented at the intra-Afghan talks, which envoy Khalilzad said would not be on the "Taliban's terms".

The US envoy likewise emphasised that those attending the intra-Afghan dialogue would be there only in their personal capacity.

"Senior (Afghan) government people are here -- the president's senior advisers... everyone, as far as the Afghan dialogue is concerned, is here in their personal capacity.

"President Ghani is quite comfortable with it," said Khalilzad.

Observers have criticised the US for allowing its own talks with the Taliban to proceed without the formal participation of the Afghan government, which the Taliban label Washington's puppet.

Khalilzad said he hoped direct negotiations between the Afghan government and the Taliban could begin "relatively soon" following the intra-Afghan summit.

"It's up to the Afghans to decide when negotiations start," he said.

US Secretary of State Mike Pompeo has previously said Washington wants a deal with the Taliban by September 1 -- ahead of Afghan elections at the end of the month.

Khalilzad said the presidential poll could still go ahead as planned on September 28 even if no deal has been reached, but reiterated hopes a deal could be clinched in time.

President Donald Trump is impatient to pull the remaining 14,000 US troops out of Afghanistan, believing nothing more can be achieved from the military operation launched after the September 11, 2001 attacks on the United States.

Trump has overturned US policy on Afghanistan's neighbour Iran, last year pulling out of a nuclear deal Tehran signed with world powers.

But Washington's envoy to the Taliban talks said the insurgents were not deterred by the US scrapping its commitment to the landmark accord.

"The Iran deal is not the first deal we've got out of," said Khalilzad.

"But no they haven't said therefore they don't want to reach an agreement with us."