Earlier Voice of America (VOA), known for its biased anti-Iran policies, reported that one of the victims, identified as Hossein J., had been arrested after taking part in the riots and unrest.
The Iranian judiciary confirmed that the person died of smoke inhalation, but stated that he was unrelated to the recent protests as he had been detained for theft a few months earlier on July 10 2022.
Tehran Prosecutor Ali Salehi had also denied the incident is related to the unrest and deadly riots in Iran that saw the detention of many people involved in the mayhem.
The fire broke out following a brawl among a number of prisoners convicted of financial crimes, leaving eight dead and dozens of inmates wounded due to smoke inhalation, some of them with serious injuries, according to officials figures.
The prisoners reportedly set fire to a warehouse full of prison uniforms, which caused the blaze, but security forces intervened to restore calm.
The authorities say the identities of the deceased have been notified to their next of kin and their names will be publicly announced after a court warrant.