July 6 (UPI) -- U.S. Special Rep. Zalmay Khalilzad said Saturday intra-Afghan dialogue is critical to the peace process.
Khalilzhad tweeted Saturday that "the most productive session to date," has been in the last six days.
"We made substantive progress on all four parts of a peace agreement: counter-terrorism assurances, troop withdrawal, participation in intra-Afghan dialogue and negotiations, and permanent and comprehensive ceasefire," he tweeted.
Still, there's more "work left to be done," he added in another tweet, as the talks will pause until Tuesday for the intra-Afghan conference for peace, which is "a critical milestone in the #AfghanPeaceProcess."
Germany and Qatar will facilitate the intra-Afghan dialogue on Sunday and Monday in Doha, Qatar.
"I want to thank #Germany and #Qatar for agreeing to host the upcoming July 7-8 intra-Afghan Dialogue Conference. This dialogue is an essential element of the four-part peace framework and an important step in advancing the AfghanPeaceProcess," Khalilzhad tweeted Monday. "Mutual acceptance, seeking consensus, and agreeing to resolve political differences is what is needed to learn from the tragedy of the last 40 years. I wish participants success."
Taliban spokesman Suhail Shaheen also said there has been a lot of progress in talks lately.
"Eighty-Ninety percent work on the peace agreement is finished," Shaheen said. "Spectacular progress made this round."
While previous rounds haven't been successful, if new talks were to produce an agreement, about 14,000 U.S. troops could leave Afghanistan.
Shaheen seemed optimistic about the future, tweeting that there had not been any obstacles yet and he hoped "work should be completed soon."
The intra-Afghan dialogue is critical because Afghan President Ashraf Ghani is adamant that an end to the 18-year-war in Afghanistan cannot be reached without his government's active involvement and the Taliban has previously refused to talk with Kabul.
The Taliban, who ruled the country from 1996 until the U.S. invasion of Afghanistan in 2001 after the 9/11 attacks, have called the Afghan government a "U.S. puppet," and refused to talk to them, which has led to the government complaining it has been sidelined in negotiations.
At least 60 Afghan delegates are reportedly taking part in the dialogue, including various stakeholders, former Islamic warriors who fought the Soviet Union in the 1980s, former government officials, former ambassadors, civil society representatives and a small number of women.
Still, the Taliban insists delegates attending the two-day talks will only do so in a "personal capacity."
Furthermore, Sediq Seddiqi, Ghani's spokesperson, told VOA the Afghan government would not attend the conference.
"No one from the Afghan government would attend the gathering to represent the Afghan government," Seddiqi said. "We believe whoever attends the gathering would be doing so in their private capacities."
Meanwhile, the Trump administration is demanding a ceasefire as violence continues, but the Taliban is demanding a timeline for U.S. troops to withdraw from Afghanistan before agreeing to ceasefire.
A car bomb explosion in the Afghan capital Monday killed dozens of Afghans and left more than 100 wounded, including many children.