Iran's judiciary said all the victims of the prison blaze had been held in a section of the prison designated for prisoners of robbery-related crimes.
Evin also holds political prisoners and many detainees facing security charges, including Iranians with dual nationality.
State media reported on Sunday that the first four deaths had been caused by smoke inhalation and that more than 60 had been injured, four of them critically.
Iran, which has blamed the violence on enemies at home and abroad, denies security forces have killed protesters.
State media said on Saturday at least 26 members of the security forces had been killed by "rioters".