Khalilzad is expected to deliver a message to government leaders that ceasefire could be extended if prisoner release process is completed by Eid al-Adha which will begin on Friday, sources said.
The Afghan government and the Taliban have announced a three-day ceasefire over the Muslim religious holiday.
Earlier on Tuesday, President Ashraf Ghani said that the government would soon complete the release of 5,000 Taliban prisoners.
Khalilzad’s visit to Kabul comes as part of a tour to five nations including also Qatar, Pakistan, Norway and Bulgaria.
“In Doha and Kabul, Ambassador Khalilzad will press for resolution of the remaining issues ahead of intra-Afghan negotiations, specifically final prisoner exchanges and reduced violence,” according to a statement from the US State Department.