"These six days have been the most productive of the rounds we've had with the Talibs... we made progress on all the issues that we have been discussing," Khalilzad said in Qatar.
The insurgents have been meeting with the US envoy in Doha to try to forge a deal that would see the US military quit Afghanistan in return for various guarantees.
Suhail Shaheen, the spokesman for the Taliban's office in Qatar, said they were pleased with the discussions so far.
"We are happy with the progress and hope the rest of the work is also done. We have not faced any obstacles yet," he tweeted.
But the talks are set to be paused for two days while another summit with Afghan representatives takes place in Qatar's capital.
"Tomorrow and the day after, because of the intra-Afghan conference, no talks will take place," Shaheen said.
US envoy Khalilzad confirmed direct US-Taliban talks will restart on Tuesday.
About 60 Afghan delegates are expected to attend Sunday's so-called intra-Afghan dialogue, 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 talks planned for Sunday and Monday will only do so in a "personal capacity".
But the US has made it clear the Taliban must talk with the Afghan government before a peace deal can be completed.
US Secretary of State Mike Pompeo has said he hopes for an agreement before September 1.