Protests have raged for a fourth-straight day across Iran as authorities confirmed three people had been killed during unrest over the death of a young woman in police custody.

The death last week of 22-year-old Mahsa Amini who was arrested by morality police for "unsuitable attire" unleashed a flood of simmering anger over numerous issues including rights, security and an economy reeling from international sanctions.

It is some of Iran's worst unrest since street clashes last year over water shortages. The Iranian government accused foreign agents and unspecified terrorists of instigating the violence.

The circumstances leading to the suspicious death in custody of 22-year-old young woman Mahsa Amini, which include allegations of torture and other ill-treatment in custody, must be criminally investigated.

In an apparent effort to defuse tensions, an aide to Iran's Supreme Leader Ayatollah Ali Khamenei paid condolences to Ms Amini's family, saying that Mr Khamenei was affected and pained by her death.

Demonstrations continued in Tehran late on Tuesday and police fired tear gas, the semi-official Fars news agency reported.

Kurdish human rights group Hengaw said three people were killed in Kurdistan on Monday when security forces opened fire.

The protests, sparked by Ms Amini's death, "also shed light on the groundswell of issues that ordinary Iranians face every day related to security, freedom", said Sanam Vakil of the Chatham House think-tank.

Ms Amini 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.