The United States had previously released a total of around 200 prisoners from its remote base on the southeast tip of Cuba where suspects were first taken bound and shackled three years ago in the wake of the US-led war in Afghanistan.
"Around 80 prisoners have been brought from Guantanamo and they will be freed today after Supreme Court officials speak to them," court spokesman Wahid Mozhda told Reuters.
Hundreds of Afghan Taliban and foreign al-Qaida fighters were captured during and after the conflict in Afghanistan and many of them were sent to Guantanamo for interrogation.
A Taliban spokesman said all Afghan prisoners should be freed.
"All the prisoners under the custody of the Americans either inside or outside Afghanistan, they are innocent people, they are not Taliban," Taliban spokesman Abd al-Latif Hakimi told Reuters by satellite telephone. "The Americans are torturing and harming those innocent people in their jails."
Human rights groups have criticised conditions at the US naval base, where Washington has classified prisoners as enemy combatants excluded from the terms of the Geneva Conventions on the treatment of prisoners of war.
Last March, some from a group of 23 Afghans freed from Guantanamo said they were mistreated, but a group of 11 freed at the request of US-backed Afghan President Hamid Karzai in September said they had been treated well.