At least 12 people have been killed in Iran, according to local news media reports, as anti-government demonstrations continued across the country for a fourth night.

Thousands have engaged in protests since the first rallies against the high cost of living on December 28, marking the biggest show of dissent in Iran since huge rallies took place in 2009.

State TV reported on Monday that 10 people were killed in several cities on Sunday, and showed footage of damage allegedly caused by protesters.

The report did not provide further details about the deaths.

Local media reports said that of those who died, six were killed in Twiserkan, in Hamedan province, and three others in Shahin Shahr, in Esfahan province.

Another person was killed in Izeh, while two others died in Dorud, in western Iran, late on Saturday.

On Monday evening, a small protest broke out in a central part of the Iranian capital, Tehran. Police used tear gas and water cannon to disperse crowds who were chanting anti-establishment slogans.

"This is better than staying silent," Milad, a young protester told Al Jazeera. His eyes were red from tear gas and he had brought masks to give to others demonstrating.

Nearby, Aslan, a 52-year-old man who was not among the protesters but was in the area, said those rallying "need a chance to show they are not happy".

"The government should let them protest," he told Al Jazeera.

Some 400 people have been arrested across Iran in the protests, state news agencies have reported.

Rouhani's first comments

On Sunday, Iran's President Hassan Rouhani said people in the country have the right to protest but warned that violence is unacceptable.

"It should be clear to everyone that we are people of freedom. According to the constitution and citizens' rights, people are free to express their criticism and to protest," Rouhani said in televised remarks, his first since the rallies started

"However, we need to pay attention to the manner of that criticism and protest. It should be in such a way that it will lead to the improvement of the people and state.

"People have the right to protest, but those demonstrations should not make the public feel concerned about their lives and security."

Iranians began protesting in the second-largest city of Mashhad, railing at the ruling religious elite, whom they blame for economic hardships and alleged corruption.

The rallies have since gained momentum and spread to other cities, including Tehran.

Several videos posted on social media have shown protesters calling for the fall of Rouhani's government.

Angry at the high cost of living, some protesters have rallied against rising prices, unemployment and economic inequality. These demonstrators hoped that Iran's nuclear deal in 2015 with world powers, which led to the lifting of many international sanctions, would ease their financial struggles.

But life for many has not improved.

"The issue is elevated expectations, that's where the danger comes in," Mohammad Ali Shabani, an Iranian political analyst and scholar, told Al Jazeera.

Shabani said that inflation had been reduced in recent years, but unemployment and the cost of living had gone up.

"People have been expecting better lives, partly as a result of Rouhani's promises in connection with the nuclear deal," he explained.

"It's not a matter of absolute poverty driving people into the streets, it's mostly about people thinking that, 'We need more than this, we were actually promised more than what's happening, we don't have the jobs that we were anticipating'."

Other protesters have said it is time for the government to focus on domestic issues, chanting anti-government slogans against the country's foreign policy, as well as Rouhani and Supreme Leader Ayatollah Ali Khamenei.

'Varied demands, varied responses'

Unlike the mass protests of in 2009 that followed the disputed re-election of then-President Mahmoud Ahmadinejad, the recent demonstrations appear to be more spontaneous, decentralised and without clear figureheads.

"We don't know who precisely is behind the protests, they do not have the same kind of leadership as in 2009," said Shabani, underlining the protesters' different grievances.

"You have varied demands, and also you have varied responses from Iranian leaders," he added.

"Initially they were opposed to high prices, some now say 'Death to Khameini' and 'Death to Rouhani', so they are targeting different political figures, different power centres and they have different demands.

"What the Iranian leaders have been saying is that we have two types of protesters out on the streets: there are some with genuine economic grievances who have the right to protest, and there are others who are after a different thing which we do not expect, referring to people who call for Khameini's death for instance, so that dynamic is quite interesting."

US watching 'very closely'

US President Donald Trump has been quick to respond to the protests, saying Washington 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," he said on Twitter on December 31.

Big protests in Iran. 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. The USA is watching very closely for human rights violations! — Donald J. Trump (@realDonaldTrump) December 31, 2017

Rouhani has since hit back at Trump, accusing him of having "forgotten that he has called the Iranian people 'terrorists' a few months ago", on Sunday.

Canada has also commented on the demonstrations, with the country's ministry of foreign affairs saying it was "closely monitoring" the protests, and calling "on the Iranian authorities to uphold and respect democratic and human rights".

"Canada is encouraged by the Iranian people who are exercising their basic right to protest peacefully," the ministry said in a short statement on December 31.

"Canada will continue to support the fundamental rights of Iranians, including the right to freedom of expression."

A spokesperson for Iran's Foreign Ministry has condemned Canada's response as "interventionist", saying it violated the country's international commitments.

"[It is] devoid of any legal justifications," Bahram Qasemi said, according to Iran's official state news agency, IRNA.