Around 200 protesters marched through downtown Tehran on Sunday, according to the conservative-linked Fars news agency, as authorities braced for a possible fourth night of unrest.

Several hundred more were shown gathering in the western city of Kermanshah, according to footage shared online by a group linked to the Revolutionary Guards.

"Contrary to rumours from hostile media, most parts of Tehran are calm. Around 200 people are occasionally chanting here and there," Fars said.

It said shops had closed early "for fear of damage to their shops by rioters".

While reports have suggested large-scale demonstrations in many towns and cities across Iran, protests have been limited in the capital city of 8.5 million people.

Students protested around the university on Saturday but were met by tear gas and a large cohort of counter-demonstrators.

Officials reported an attack on a town hall in central Tehran and multiple incidents of vandalism through the night.

The city's chief prosecutor Abbas Jafari Dolatabadi said a "certain number of people" had been arrested, without giving a figure.

"The trouble-makers are not part of the people. Actions against security, notably setting fire to buildings and public utilities are not normal crimes and the judiciary will react with determination against them," he said.

The government has warned protesters will "pay the price" for further unrest, and blocked access to social media sites earlier on Sunday, accusing them of fomenting disorder.