Crowds cheered when women burned their hijabs on a bonfire in Sari on Tuesday, as the unrest continued for a fifth night and spread to more cities.
Activists said two male protesters were shot dead by security forces in Urmia and Piranshahr, in the north-west.
A police assistant was also reportedly killed in Shiraz, in the south.
At least six people are now believed to have been killed since protests against the hijab laws and the morality police erupted after the death of Mahsa Amini.
The 22-year-old Kurdish woman from the north-western city of Saqez died in hospital on Friday, after spending three days in a coma.
She was with her brother in Tehran when she was arrested by morality police, who accused her of breaking the law requiring women to cover their hair with a hijab, or headscarf, and their arms and legs with loose clothing. She fell into the coma shortly after collapsing at a detention centre.
There were reports that police beat Ms Amini’s head with a baton and banged her head against one of their vehicles, Acting UN High Commissioner for Human Rights Nada al-Nashif said.
The police have denied that she was mistreated and said she suffered “sudden heart failure”. But her family has said she was fit and healthy.
“Mahsa Amini’s tragic death and allegations of torture and ill-treatment must be promptly, impartially and effectively investigated by an independent competent authority, that ensures, in particular, that her family has access to justice and truth,” Ms Nashif said.
She noted that the UN had received “numerous, and verified, videos of violent treatment of women” as morality police expanded their street patrols in recent months to crack down on those perceived to be wearing “loose hijab”.
“The authorities must stop targeting, harassing, and detaining women who do not abide by the hijab rules,” she added, calling for their repeal.
An aide to Iran’s Supreme Leader Ayatollah Ali Khamenei paid a visit to Ms Amini’s family on Monday and told them that “all institutions will take action to defend the rights that were violated”, state media reported.
Senior MP Jalal Rashidi Koochi publicly criticised the morality police, saying the force was a “mistake” as it had only produced “loss and damage” for Iran.
What are Iran’s hijab laws?
Following the 1979 Islamic Revolution, authorities in Iran imposed a mandatory dress code requiring all women to wear a headscarf and loose-fitting clothing that disguises their figures in public.
Morality police – known formally as “Gasht-e Ershad” (Guidance Patrols) – are tasked, among other things, with ensuring women conform with the authorities’ interpretation of “proper” clothing. Officers have the power to stop women and assess whether they are showing too much hair; their trousers and overcoats are too short or close-fitting; or they are wearing too much make-up. Punishments for violating the rules include a fine, prison or flogging.
In 2014, Iranian women began sharing photos and videos of themselves publicly flouting the hijab laws as part of an online protest campaign called “My Stealthy Freedom”. It has since inspired other movements, including “White Wednesdays” and “Girls of Revolution Street”.
Ms Nashif also expressed alarm at “the reported unnecessary or disproportionate use of force” against the thousands of people who have taken in part in protests since Mahsa Amini died.
Hengaw, a Norway-based organisation that monitors human rights in predominantly Kurdish areas of Iran, said a 16-year-old boy and a 23-year-old man were killed when security forces opened fire at protesters on Tuesday night in Piranshahr and Urmia, which are both in West Azerbaijan province.
The group had also reported that three male protesters had been shot and killed by security forces in the neighbouring province of Kurdistan on Monday – one in Saqez, Ms Amini’s home city, and two others in the towns of Divandarreh and Dehgolan – as the unrest escalated. It had previously reported the death of a second man in Divandarreh, but relatives said he was in a critical condition in hospital.
The state-run Irna news agency meanwhile said a police assistant died of injuries he sustained in violent clashes with protesters in the southern city of Shiraz on Tuesday.
Irna also reported that protests took place in 15 cities overnight, including Tehran, Mashhad in the north-east, Rasht in the north, and the central cities of Kerman and Isfahan. Police used tear-gas and made arrests to disperse crowds who blockaded streets, hurled stones and set fire to police vehicles, it added.
In the capital, videos posted online showed women taking off their headscarves and shouting “death to the dictator” – a chant often used in reference to the Supreme Leader. Others shouted “justice, liberty, no to mandatory hijab”.
A woman who took part in a protest on Monday in Rasht sent BBC Persian photographs of what she said were bruises she suffered as a result of being beaten by riot police with batons and hoses.
“[The police] kept firing tear gas. Our eyes were burning,” she said. “We were running away, [but] they cornered me and beat me. They were calling me a prostitute and saying I was out in the street to sell myself.
Another woman who protested in Isfahan told the BBC’s Ali Hamedani: “While we were waving our headscarves in the sky I felt so emotional to be surrounded and protected by other men. It feels great to see this unity. I hope the world supports us.”
Tehran Governor Mohsen Mansouri tweeted on Tuesday that the protests were “fully organised with the agenda to create unrest”, while state TV alleged that Ms Amini’s death was being used as an “excuse” by Kurdish separatists and critics of the establishment.
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