The death of Mahsa Amini last week after her arrest by Iran's morality police has sparked anger and anxiety among many women in the Islamic republic.

"I'm frightened," said Nazanin, a 23-year-old nurse from Tehran, who said she is now far more careful about how she wears her headscarf to avoid run-ins with the police unit responsible for enforcing a strict Islamic dress code for women.

Amini, a Kurd, had been detained for allegedly wearing a hijab headscarf in an "improper" way, and died at a Tehran hospital after having spent three days in a coma.

Public anger has flared over her death, and at least six protesters have been killed in nationwide demonstrations, according to Iranian officials.

The behaviour of the morality police – known formally as the Gasht-e Ershad or "Guidance Patrol" – "isn't right", Nazanin said.

"They shouldn't confront people at all" or interfere with how women dress, she added. "I don't understand why they do it," she said, insisting that "everyone respects the law".

"Hijab is a choice," said Mahtab, a 22-year-old make-up artist, wearing an orange headscarf outside her shop in an affluent neighbourhood in Tehran's north.

"It shouldn't be forced. I like to wear it... others prefer a chador," she added, referring to the conservative black full-body dress.

Mahtab is "afraid of seeing" the morality police, but said she has not changed "at all" how she dresses.

However, she said she would not "dare" take part in the many demonstrations in the capital and more than a dozen other cities since Amini's death was announced last Friday, and she called the protesters "brave".

In Iran, women – regardless of their faith – are required to cover their hair, and the morality police bans them from wearing coats above the knee, tight trousers, bright colours or torn jeans.

Activists said Amini had suffered a fatal blow to the head, a claim denied by officials, who have announced an investigation.

In Turkey, a woman cut her hair as dozens of others cheered at a protest held outside Tehran's Istanbul consulate in solidarity with Mahsa Amini.

Turkish and Iranian women outside the consulate brandished portraits of Amini.

"Iranian women's fight for freedom is our own fight. Long live our international solidarity!" one protester said. (AFP)