The team members, including Andrew North, a British citizen and former BBC reporter, were on assignment with the United Nations High Commissioner for Refugees and were detained in Kabul in recent days.
Taliban spokesman Zabihullah Mujahid says life is returning to normal in the country but chaos at the airport remains a problem. Many Afghans are desperate to flee the Taliban takeover of the country.
Speaking on Tuesday at a first press conference since taking power, Taliban spokesman Zabihullah Mujahid promised that the new government would not turn the world's leading producer of opium into a fully-fledged narco-state.
RSF, a Paris-based media freedom organisation, said the assurances were given by Zabihullah Mujahid in a conversation on Sunday as the extremist group was taking over the capital Kabul.
President Ashraf Ghani condemned the attack "in the strongest possible terms" in a statement from the presidential palace, only a few hundred metres away from the scene of the blast in central Kabul.