Taliban leaders imposed a ban on the ICRC and the World Health Organisation (WHO) earlier in April saying the organisations were carrying out "suspicious" activities during vaccinations campaigns and not sticking to their declared missions.
The Taliban on Sunday revoked their ban on the International Committee of the Red Cross (ICRC) in Afghanistan and gave a guarantee of security for its staff doing humanitarian work in areas under their control.
Taliban leaders imposed a ban on the ICRC and the World Health Organisation (WHO) in April saying the organisations were carrying out "suspicious" activities during vaccinations campaigns and not sticking to their declared missions.
"The Islamic Emirate restores the former security guarantees to ICRC in Afghanistan and instructs all mujahideen to pave the way for ICRC activities and be mindful of security to this committee's workers and equipment," Taliban spokesman Zabihullah Mujahid in a statement.
The Taliban refer to themselves as the Islamic Emirate of Afghanistan.
The spokesman did not refer to the WHO in his statement.
Officials at ICRC and WHO in Kabul were not immediately available for comment.
The WHO has been carrying out a vaccination campaign in Afghanistan, one of the last countries in the world where polio is endemic.
The ICRC has been providing medical support for more than 30 years.
Aid groups operating in Afghanistan stress that they do not take sides.
The ICRC in particular is known for its strict neutrality in conflicts.
It operates in Taliban-controlled areas with a guarantee of safety and helps to repatriate bodies from both sides after fighting between the militants and the Afghan army.
The Taliban control or contest more than half of Afghanistan's 410 Afghan districts.