An Iranian bank manager who served an unveiled woman has been fired, local media reported on Sunday, as demonstrations triggered by the mandatory head covering rule shake the Islamic republic.

Women in the country of more than 80 million people are required to cover their heads, necks and hair, a law enforced by the country's morality police.

The September 16 death in morality police custody of Mahsa Amini, 22, for allegedly breaching the dress code rules, sparked nationwide demonstrations which authorities call "riots".

Mehr news agency reported that the bank manager in Qom province, near the capital Tehran, "had provided bank services on Thursday to an unveiled woman".

As a result he was "removed from his position by order of the governor," Mehr quoted deputy governor Ahmad Hajizadeh as saying.

Mehr said video of the unveiled woman "elicited a lot of reaction on social media".

In Iran most banks are state-controlled and Hajizadeh said it is the responsibility of managers in such institutions to implement the hijab law.

Dozens of people, mainly protesters but also members of the security forces, have been killed during the demonstrations, which Iran says are encouraged by its Western "enemies".

The hijab became mandatory four years after the 1979 revolution that overthrew the US-backed monarchy and established the Islamic Republic.

Later, with changing clothing norms, it became commonplace to see women in tight jeans and loose, colourful headscarves.

But in July this year ultra-conservative President Ebrahim Raisi called for mobilisation of "all state institutions to enforce the headscarf law".

Many women continued to bend the rules, however.