"Death to the dictator" and "Woman, life, freedom," protesters could be heard shouting in video footage shared online, during the biggest wave of protests to rock the country in almost three years.
Among those killed in clashes have been police and militia officers, state TV reported, while overseas-based human rights groups reported many more deaths, which could not be independently verified.
Security forces have fired at crowds with birdshot and metal pellets, and also deployed tear gas and water cannon, according to Amnesty International and other human rights groups.
There were fears violence could escalate further after Iranian authorities restricted internet access and blocked messaging apps including WhatsApp and Instagram, as they have done before past crackdowns.
Some women have burnt their scarves and symbolically cut their hair in protest at the strict dress code, in defiant actions echoed in solidarity protests abroad from New York to Istanbul.
Activists have said that Amini, whose Kurdish first name is Jhina, after her detention in Tehran suffered a fatal blow to the head -- a claim denied by officials, who have announced an investigation.
Iranian women on the streets of Tehran told AFP they were now more careful about their dress to avoid run-ins with the morality police.
"I'm frightened," said the nurse Nazanin, 23, who asked to be identified by her first name only for safety reasons, adding that she believed the morality police "shouldn't confront people at all".
US President Joe Biden in an address to the UN General Assembly on Wednesday said that "we stand with the brave citizens and the brave women of Iran who right now are demonstrating to secure their basic rights".
Iran's ultra-conservative President Ebrahim Raisi, speaking later in the same forum, complained of a "double standard" and pointed to Israeli actions in the Palestinian territories and the deaths of indigenous women in Canada.
The protests come at a particularly sensitive time for the leadership, as the Iranian economy remains mired in a crisis largely caused by international sanctions over its nuclear programme.
Unprecedented images have shown protesters defacing or burning images of supreme leader Ayatollah Ali Khamenei and late Revolutionary Guards commander Qasem Soleimani.
The wave of unrest "is a very significant shock, it is a societal crisis," said Iran expert David Rigoulet-Roze of the French Institute for International and Strategic Affairs.
The protests are among the most serious in Iran since November 2019 unrest sparked by a sharp rise in petrol prices. The crackdown then killed hundreds, according to Amnesty.
Demonstrators have hurled stones at security forces, set fire to police vehicles and garbage bins, and chanted anti-government slogans, the official IRNA news agency said.
On Thursday, Iranian media said three militiamen "mobilised to deal with rioters" were stabbed or shot dead in northwestern Tabriz, central Qazvin and northeastern Mashhad.
UN human rights experts condemned the "use of physical violence against women" and the "state-mandated internet disruptions" which they said were usually part of larger efforts "to stifle... free expression... and to curtail ongoing protests",
Iran's Fars news agency reported that "in accordance with a decision by officials, it has no longer been possible to access Instagram in Iran since (Wednesday) evening and access to WhatsApp is also disrupted".
The two apps were the most widely used in Iran after the blocking of other platforms in recent years, including Facebook, Twitter, Telegram, YouTube and Tiktok.