A leading Iranian cleric has urged authorities "to listen to the people", as protests ignited by a young woman's death in morality police custody show no sign of letting up.

Demonstrators have taken to the streets of major cities across Iran, including the capital Tehran, for 10 straight nights since the death of Mahsa Amini.

The 22-year-old was pronounced dead on September 16, three days after her arrest in the capital for allegedly breaching Iran's strict dress code for women.

"The leaders must listen to the demands of the people, resolve their problems and show sensitivity to their rights," said Grand Ayatollah Hossein Nouri Hamedani in a statement posted on his website Sunday.

The powerful 97-year-old cleric has long been aligned with the country's ultra-conservative establishment and strongly backed supreme leader Ayatollah Ali Khamenei on several occasions -- notably during the 2009 protests against the reelection of former president Mahmoud Ahmadinejad.

"Any insult to the sanctities and any attack on the rights of the people and public property are condemned," Hamedani added.

At least 41 people have been killed since the protests began on September 16, mostly protesters but including security forces, according to an official toll.

The protests have spread to several cities, where demonstrators have shouted slogans against the authorities, according to local media.

More than 1,200 demonstrators, reformist activists and journalists have been arrested during the mostly night-time demonstrations across the country.

On September 18, Grand Ayatollah Assadollah Bayat Zanjani, a cleric seen as close to the reformists, denounced what he said were "illegitimate" and "illegal" actions behind the "regrettable incident" of Amini's death.