A video image shows Iranian protesters gathered on a road leading to the Evin prison in Tehran. AFP

The judiciary said four of those injured in Saturday's fire were in critical condition and those killed had died of smoke inhalation, Iranian state media reported.

The fire at Tehran's notorious Evin prison came amid ongoing unrest sparked by the death of 22-year-old Mahsa Amini while in the custody of Iran's morality police a month ago.

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The protests have turned into one of the boldest challenges to the clerical leadership since the 1979 revolution, and have been met with a brutal crackdown.

Before the authorities published the death toll from the fire, families of some political detainees took to social media to call on the authorities to ensure the safety of prisoners at Evin, which in 2018 was blacklisted by the U.S. government for "serious human rights abuses".

This image grab image show a fire truck driving toward the scene of a fire at the Evin prison in Tehran. AFP

Iranian authorities said on Saturday that a prison workshop had been set on fire "after a fight among a number of prisoners convicted of financial crimes and theft". Evin holds many detainees facing security charges, including Iranians with dual nationality.

The footage of Evin aired on state television hours later showed firefighters inspecting a workshop with fire damage to the roof. It also showed inmates in their wards apparently "sleeping as calm has been restored".

Atena Daemi, a human rights activist, said that relatives of prisoners held in the women's section had gathered at the prison for routine visiting hours, but that the authorities had denied them access, resulting in a standoff.

The relatives were told that the prisoners were "fine, but the phones are broken", according to Daemi.

"When the families said they would not leave until they (prisoners) call, give them mobile phones to call, security guards confronted the families," she tweeted.

Reuters