The Taliban in a statement on Sunday asked the International Committee of the Red Cross, ICRC, to resume its activities in Afghanistan.
The group warned the ICRC on April 13 to abandon its activities in the country.
The statement was made after talks between representatives of the Taliban and the International Committee of the Red Cross were held in Qatar.
The ICRC halted its activities in many parts of the country nearly six months ago after receiving Taliban threats.
On April 13, the Taliban also threatened the World Health Organization with targeting if it did not stop its activities in Afghanistan.
The ICRC has operated in Afghanistan for over 30 years and has been primarily focused on providing assistance to war prisoners and war victims.
The WHO provides polio vaccination services to children, along with other healthcare services to Afghans nationwide.