The two sides met on Tuesday and are scheduled to meet again on Wednesday for further talks, Afghanistan’s Office of the National Security Council said on Twitter.
“The two sides held face-to-face negotiations about the release of Afghan National Defense and Security Force personnel as well as Taliban prisoners,” the Security Council said.
It was the first time the Taliban have been invited to Afghanistan’s capital to meet directly with government officials since they were toppled in the US-led invasion of 2001.
The two sides had spoken previously in a video conference to discuss the prisoner issue.
Taliban spokesman Zabihullah Mujahid told the AFP news agency that a “technical team” was in Kabul purely to facilitate the prisoner swap, and not for additional negotiations.
“The prisoners to be released should be those whose names are on the list … that is why our technical team is there … it is not a negotiation, and there will be no political talks there,” Mujahid said.
The United States signed a deal with the Taliban in February that promised the withdrawal of US and foreign troops from Afghanistan by July next year, provided the Taliban start talks with Kabul and adhere to other guarantees.
The deal required the Afghan government – which was not a signatory to the accord – to free 5,000 Taliban prisoners and for the group to release 1,000 pro-government captives in return.
The swap was supposed to have taken place by March 10, at which point peace talks between the Taliban and the government were meant to begin.
But Kabul has been gripped by fresh political bickering and infighting and the prisoner release issue was delayed.
The security situation has also deteriorated with a series of Taliban attacks killing at least 20 members of Afghan security forces on Sunday.
On Wednesday, a roadside bomb killed at least seven civilians including six children in southern Helmand province, which authorities blamed on the Taliban.