Al-Jazeera correspondent in Afghanistan quoted a spokesman for the Taliban political office in Qatar, Suhail Shaheen, as saying that the Doha talks between the movement and the American envoy to Afghanistan Zalmay Khalilzad were continuing.
Shaheen said that the talks have not yet made significant progress due to the new demands made by the United States, without clarifying what those demands are.
On the other hand, a source close to the talks said that the Taliban had agreed to reduce violence in Afghanistan as a preliminary measure.
But the American envoy calls for a complete cease-fire, while the movement believes that it will consider it after signing the final agreement.
Khalilzad met after his arrival yesterday in the Afghan capital, the cable of Afghan President Muhammad Ashraf Ghani.
A statement said Khalilzad was awaiting a clear response from the Taliban about the ceasefire.
Reuters reported late last month that the Afghan Taliban would reduce attacks on Afghan forces, and would hold talks with government officials if they reached an agreement with US negotiators in the ongoing peace talks in Doha.
The movement announced at the time that one of its senior officials had met American officials in the Qatari capital to discuss signing a peace agreement, and the Al-Jazeera correspondent in Afghanistan stated that the matter concerned Mullah Abdul Ghani Brader, the movement's political affairs deputy who met in Doha, American envoy Zalmay Khalilzad.
A source on the island also said that the commander of US forces in Afghanistan, General Skat Miller, joined Khalilzad.
"The United States wanted to declare a ceasefire during the peace talks, which we rejected ... The (movement) Shura Council agreed to a ceasefire on the day the peace agreement was signed," a senior Taliban commander said.
He added that once a ceasefire agreement is reached, the Taliban and the Afghan government can hold a direct meeting in Germany.
The movement had previously refused to enter into talks with the government.