Earlier, following second virtual meeting between the Afghan government and the Taliban last week, the group and US special envoy Zalmay Khalilzad said the sides agreed to begin prisoner releases on March 31.
On Sunday, the sides met again through video link.
“There is no prisoner release happening tomorrow. Taliban agreed in the video conference yesterday to send a team to Kabul to hold further technical discussions with the government of the Islamic Republic of Afghanistan,” Javid Faisal, a spokesman for National Security Council, said on Twitter.
According to a statement from the council, The Taliban will send their technical team to Kabul with assistance from ICRC, and the government will host the Taliban team in Bagram to continue work on prisoner release.
The Taliban have demanded that 5,000 prisoners must be freed all at once as a pre-condition to peace talks, while the Afghan government is seeking a phased and conditional release.
A deal the insurgents signed with the United States in Doha last month for a US troop withdrawal specified the freeing of up to 5,000 prisoners by March 10. The Taliban would free 1,000 prisoners, according to the deal.