Geneva: The UN decried Tuesday Mahsa Amini's death in custody after she was arrested by Iran's "morality police" and the violent crackdown on protests over her death, demanding an independent investigation.

"Acting UN High Commissioner for Human Rights Nada Al-Nashif today expressed alarm at the death in custody of Mahsa Amini... and the violent response by security forces to ensuing protests," the rights office said in a statement.

Public anger has grown since authorities Friday announced Amini's death in hospital after three days in a coma, following her arrest by Tehran's morality police during a visit to the capital on September 13.

The police unit is responsible for enforcing Iran's strict dress code for women, including the wearing of the headscarf in public.

Demonstrations were held in Tehran, including in several universities, and the second city Mashhad, according to the Fars and Tasnim news agencies.

There are reports that the 22-year-old was "beaten on the head with a baton, and her head was banged against the vehicle by the so-called morality police", the UN statement said.

The authorities had said she died of natural causes.

"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," Al-Nashif said in the statement.

UN rights office spokeswoman Ravina Shamdasani meanwhile told reporters that Iranian security forces had reportedly responded to the massive protests that erupted over Amini's death "with live ammunition".

As many as five people were known to have died in that crackdown, she said.

In her statement, Al-Nashif also voiced concern at the compulsory veiling laws in Iran, where appearing in public without a hijab is punishable by imprisonment.

"The authorities must stop targeting, harassing, and detaining women who do not abide by the hijab rules," the acting UN rights chief said, calling for the repeal of all discriminatory laws and regulations that impose mandatory hijab.