Demonstrations continued in Tehran late on Tuesday and police fired tear gas, the semi-official Fars news agency reported.
Tehran Governor Mohsen Mansouri accused foreign agents of fomenting the violence in the country's capital.
He said citizens of three countries were arrested during gatherings overnight, the Iranian state news agency IRNA said.
The unrest is some of Iran's worst since street clashes last year over water shortages and reflects popular discontent not only over women's rights but also over security and an economy reeling from international sanctions.
In an apparent effort to defuse tensions, an aide to Iran's supreme leader paid condolences to the family of the woman killed in custody in Tehran after morality police arrested her for "unsuitable attire".
Kurdish human rights group Hengaw said three people were killed in Kurdistan on Monday when security forces opened fire.
The governor of Kurdistan province confirmed that three people were killed but said the deaths were suspicious and did not say who was responsible for them.
"A citizen of (the city of) Divandarreh was killed with a weapon that isn't used by the armed forces. Terrorist groups are looking to kill," Esmail Zarei Koosha said in comments reported by the semi-official Fars news agency.
Mahsa Amini, 22, from Iran's Kurdistan province, fell into a coma and died while waiting with other women held by the morality police, who enforce strict rules in the Islamic Republic requiring women to cover their hair and wear loose-fitting clothes in public.
Amini's father has repeatedly said his daughter had no health problems, adding that she had suffered bruises to her legs.
He held the police responsible for her death.
Demonstrations broke out in Kurdistan and spread on Monday and Tuesday to several other provinces in northwestern Iran.
The most violent unrest has taken place in the Kurdistan region.
Videos posted on social media have shown demonstrations in numerous cities, with women waving their headscarves and protesters facing off with security forces.
The protests, sparked by Amini's death, "also shed light on the groundswell of issues that ordinary Iranians face every day related to security, freedom," Sanam Vakil of the Chatham House think-tank said.
"I don't think this is an existential challenge to the regime... because the system in Iran has a monopoly of force, a well-honed security strategy that it is already implementing," she added.
Supreme Leader Ayatollah Ali Khamenei's representative in the Kurdistan province, Abdolreza Pourzahabi, paid a two-hour visit to Amini's family home on Monday, the Tasnim news agency said, citing comments from Pourzahabi that were also reported by the state news agency.
Pourzahabi told Amini's family "all institutions will take action to defend the rights that were violated" and that he was sure Khamenei was "also affected and pained" by her death.
"As I promised to the family of Ms Amini, I will also follow up the issue of her death until the final result," Pourzahabi said.
Protesters marched through Tehran's Grand Bazaar on Monday chanting "Mahsa Amini, Rest in Peace," according to a video posted by the widely-followed 1500tasvir Twitter account, which publishes footage it says it receives from the public.
In one large protest in Tehran, a crowd of demonstrators wearing black shouted, "Oh the day when we will be armed," according to another video posted by 1500tasvir overnight.
Reuters was unable to verify the videos.
By late on Tuesday demonstrations had spread to a number of other cities, mostly in northwestern Iran, according to 1500tasvir.
Hengaw said there were protests in 13 cities on Monday and that 250 people had been arrested.
Reuters could not independently verify those reports.
In Gilan province, police arrested 22 people for destroying public property, the deputy police commander said.
