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.