The eighth round of talks in Doha concluded after midnight on Monday, reports TOLO News.
In a tweet on Monday, US Special Representative for Afghanistan Reconciliation Zalmay Khalilzad said that the talks which began on August 3 have been productive.
Khalilzad said he was returning to Washington for consultations on next steps in the peace process, adding that the US was "working hard toward a lasting and honourable peace agreement and a sovereign Afghanistan which poses no threat to any other country".
Taliban spokesman Suhail Shaheen said in a tweet that negotiators from the two sides would now consult with their leadership about the details of the topics which came under discussion in the talks.
"The agreement is expected to be signed next week in the presence of representatives of neighbouring and regional countries including delegations from NATO and the international community," TOLO News quoted political analyst Faiz Mohammad Zaland as saying on Monday.
Since his appointment to the post last September, Khalilzad has conducted eight round of talks with the Taliban in Doha and the United Arab Emirates (UAE), but these discussions in some stage followed strong reactions from Afghan President Ashraf Ghani whose administration has been out of the negotiations as the Taliban has refused to attend meetings with Kabul officials.
On August 9, a former Taliban member told TOLO News that the two sides were likely sign a peace deal after Eid-al-Adha, at the end of this week.
( With inputs from IANS )