So far, neither side has reached a breakthrough, though both hope talks will conclude in the coming few days, Suhail Shaheen, spokesman of Afghan Taliban political office in Doha told Anadolu Agency.
"The US agreed to withdraw its troops from Afghanistan and resolve the Afghan issue peacefully," Shaheen said.
However, he refused to give details about a timeline in which the US forces would leave the country.
The ninth round of US-Taliban talks resumed on Thursday in Qatar's capital Doha to find a peaceful resolution to Afghanistan's long-running conflict.
Deal with US will not stop attacks on Afghan forces: Taliban
Asked whether the Taliban would sit with the Afghan government once peace talks were complete with US officials, Shaheen reiterated his group's stance and said, "Of course we will talk with all Afghan sides. That also includes the Afghan administration but it will be one of the sides and a party of the conflict, not as the government."
The Taliban have been holding peace talks with the US for nearly a year but refuse to recognise or negotiate with the Afghan government.
However, the Taliban have said they would invite all other Afghan groups to become part of the government after a peace agreement was reached with Washington.
"Of course, we want an Islamic government in Afghanistan participated in by all Afghans, from all ethnicities, all walks of life, all groups so it will be a very strong Islamic government," Shaheen noted.
Earlier on Saturday, some media outlets reported that an agreement between the US and Taliban had been reached and that both sides agreed to establish an interim government in Kabul.
US, Taliban resume push for peace at Doha talks
However, US peace negotiator Zalmay Khalilzad and the Taliban later rejected the reports.
Presidential elections are also slated for September 28 in the country but are expected to be overshadowed by the US-Taliban talks.
On Saturday, top US diplomat in Kabul Ambassador John Bass said that elections should be held on their scheduled time if there were to be a hurdle in the way of the peace process.
"Both [peace process and elections] are important for the United States. Peace is our highest priority because it is also the highest priority of the Afghan people.
And every day, we have Afghans telling us that peace is their highest priority," Bass said.
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