Red Cross staff, Syrian Red Crescent workers and representatives of the World Health Organization have been told to leave eastern Aleppo.
"The evacuations have been halted," Middle East spokesman for the ICRC, Ralph El Hage, told CNN.
"We are hoping the parties reach an agreement so we can move forward with the evacuation."
Syria's state news agency reported that the al Nusra Front had blocked the exit of 1,250 civilians in Aleppo.