Rouhani supports protesters' rights

President Hassan Rouhani has shown support for the rights of demonstrators taking part in mass protests across the country, while also warning against turning to violence.

"We are a free country, and therefore the people have a right to express themselves," said Rouhani in his first public reaction to the protests, which entered their fourth day on Sunday.

Rouhani warned that riots could endanger the security of the country and its people, and said protests should be conducted peacefully and through legal channels, echoing earlier government sentiments.

Addressing a session of cabinet, Rouhani added that "anyone who calls the Iranian people terrorists does not have the right to sympathise for the people," in remarks quoted by state news agency IRNA and seen to address US President Donald Trump.

Trump has repeatedly written about the protests in recent days and warned again on Sunday that "the USA is watching very closely for human rights violations".

"The people are finally getting wise as to how their money and wealth is being stolen and squandered on terrorism. Looks like they will not take it any longer," wrote Trump, who has threatened to leave the 2015 Iran nuclear deal.

The "long-repressed" Iranian people were "finding their voice," the US ambassador to the UN, Nikki Haley, said on Twitter.

Government on Sunday stepped up efforts to calm down the unrest. "Resolving problems with violence and terror is not an option," said Interior Minister Abdolreza Rahmani Fazli.

"We can't, and won't, allow this," he added, noting that there had already been fatalities.

Anyone who chooses to violate the law will have to face the consequences, Fazli added, noting that there are legal avenues for people to use if they want to take issue with official policy.