Taliban spokesman Zabihullah Mujahid confirmed the team's arrival in a tweet. It marked the first time a Taliban delegation has been in Kabul since the group was driven out by the U.S. -led coalition in November 2001.
There was no immediate comment from the Afghan government on the team's arrival.
On Monday, Jawed Faisal, spokesman for the Afghan National Security Adviser's office, said Afghan officials and the Taliban agreed during a video conference that the insurgent group should send a technical team to Kabul for face-to-face discussions on the release of Taliban prisoners. The International Committee of the Red Cross agreed to assist the team in getting to Kabul.
The prisoner release is part of a peace deal signed last month by the Taliban and U.S. that calls for the government's release of 5,000 Taliban and the Taliban's release of 1,000 government personnel and Afghan troops.
Afghanistan's political turmoil and the rivalry between Ghani and Abdullah have impeded each step of talks with the Taliban. Negotiations between the Taliban and the government are supposed to come next under the peace agreement.
U.S. Secretary of State Mike Pompeo, speaking to reporters at a news conference in Washington on Tuesday, said progress was being made and pointed to plans for prisoner releases as well as Ghani's announcement last week of his 21-member team to negotiate peace with the Taliban.
The peace deal calls for the eventual withdrawal of all 13,000 U.S. soldiers from Afghanistan in exchange for guarantees from the Taliban that they will fight other militant groups, including the Islamic State group. The deal has been touted as Afghanistan's best chance yet for ending its relentless wars.
Associated Press writer Matthew Lee in Washington contributed to this report.