Iranian authorities have not published an official death toll but said three security personnel have been killed. BBC Persian has so far confirmed the deaths and identities of 20 people.
HRANA also said that more than 60 protesters had been injured and 2,076 arrested during the unrest, which was sparked by an economic crisis and has spread to 27 of 31 provinces.
On Tuesday evening, Iranian semi-official media reported that a policeman was shot dead by what they called "rioters" in Malekshahi in the western province of Ilam, where there have been widespread protests and a violent crackdown by security forces in recent days.
Earlier, security forces were filmed firing tear gas during clashes with protesters who chanted slogans against Iran's clerical rulers at Tehran's Grand Bazaar.
The protests began on 28 December, when shopkeepers took to the streets of the capital to express their anger at another sharp fall in the value of the Iranian currency against the US dollar on the open market.
The rial has sunk to a record low over the past year and inflation has soared to 40% as sanctions over Iran's nuclear programme squeeze an economy also weakened by mismanagement and corruption.
University students soon joined the protests and they began spreading to other cities.
On Friday, President Donald Trump threatened US intervention if Iranian security forces killed peaceful protesters, declaring: "We are locked and loaded and ready to go."
The following day, Iran's Supreme Leader Ayatollah Ali Khamenei - who has ultimate power - said that "rioters should be put in their place" and vowed not to "yield to the enemy".
Judiciary chief Gholamhossein Mohseni Ejei echoed the comments on Monday, saying authorities would listen those who "legitimately and rightly have concerns about their livelihood" but also show no leniency towards "rioters".
UN Secretary General Antonio Guterres was "deeply saddened by the reported loss of life and injuries resulting from clashes between security forces and protesters", and "underscores the need to prevent any further casualties", his spokesman Stephane Dujarric told reporters.
"All individuals must be allowed to protest peacefully and express their grievances," he added.