Fresh protests broke out as night fell in Tehran on Monday, local media reported, a day after 10 people were killed in violence across the country.

The latest demonstrations came despite President Hassan Rouhani's vow that the nation would deal with "rioters and lawbreakers".

US President Donald Trump, who has repeatedly criticised Tehran over four days of demonstrations, said it was "time for a change" and that the Iranian people were "hungry" for freedom.

Restrictions remained on reporting inside Iran, but social media reported a heavy police presence on the streets of central Tehran as small groups of protesters were seen running and chanting anti-regime slogans.

It followed the deadliest night yet on Sunday as state television reported six people killed by gunfire in the western town of Tuyserkan, and a local lawmaker said two people had been shot dead in the southwestern town of Izeh.

Two others, including a teenage boy, were run down and killed by a fire engine protesters stole in the western town of Dorud, the state broadcaster said, bringing the total death toll in the protests to 12.

Rouhani tried to play down the unrest which began in second city Mashhad last Thursday and quickly spread across the country to become the biggest test for the regime since mass protests in 2009.

"This is nothing," Rouhani said in a statement on the presidency website.

"Our nation will deal with this minority who chant slogans against the law and people's wishes, and insult the sanctities and values of the revolution," he said.

Pro-regime rallies were held across several towns and cities, but videos on social media showed seemingly widespread anti-government protests on Sunday in cities including Kermanshah, Khorramabad and Shahinshahr.

A school for clergy and government buildings were torched in the northwestern town of Takestan and videos showed police using tear gas and water cannon to disperse a small protest in Tehran's Enghelab Square on Sunday evening.

The authorities did not give details on who was responsible for the fatal shootings.

The authorities have confirmed more than 400 arrests since the outbreak of the unrest, of whom around 100 have been freed.

Judiciary chief Ayatollah Sadegh Larijani joined Rouhani in warning against illegal action.

"Those who have rightful demands must be guided in lawful ways and those who riot and commit sabotage and chaos and set fire to public property... must be confronted decisively," he told the state broadcaster.

"The country must have discipline," Larijani added.

Verifying rumours and videos remained challenging because of travel restrictions and sporadic blocks on mobile internet and popular social media sites including Telegram and Instagram.

The protests began as demonstrations against economic conditions in second city Mashhad on Thursday but quickly turned against the Islamic regime as a whole, with thousands marching in towns across Iran to chants of "Death to the dictator".

Trump, a fierce critic of Tehran, used one of his first tweets of 2018 to again lash out at a favourite target.

"Iran is failing at every level despite the terrible deal made with them by the Obama administration," Trump tweeted, referring to the nuclear pact agreed under his predecessor Barack Obama.

"The great Iranian people have been repressed for many years. They are hungry for food & for freedom. Along with human rights, the wealth of Iran is being looted. TIME FOR CHANGE!"

After initial silence, state media began showing some footage of the demonstrations on Sunday, focusing on young men attacking banks and vehicles, an attack on a town hall in Tehran and images of a man burning the Iranian flag.

Rouhani came to power in 2013 promising to mend the economy and ease social tensions, but high living costs and a 12 percent unemployment rate have left many feeling that progress is too slow.

"We have no problem bigger than unemployment. Our economy needs an operation. We must all stand together," Rouhani acknowledged on Monday.

The authorities have blamed external forces for fomenting violence, saying the majority of social media reports were emanating from regional rival Saudi Arabia or exile groups based in Europe.

Authorities ruthlessly put down the 2009 protests, which followed a disputed presidential election that gave hardliner Mahmoud Ahmadinejad a second term. At least 36 people were killed in the 2009 unrest, according to an official toll, while the opposition says 72 died.

In the years since, many middle-class Iranians have abandoned hope of securing change from the streets.

But low-level strikes and demonstrations have continued, with groups such as bus drivers, teachers and factory workers regularly protesting against unpaid wages and poor conditions.