Government restricts access to the popular photo sharing and messaging apps Instagram and Telegram on mobile phones in a bid to head off further protests.
At least two demonstrators have died and more than 250 arrested in Iran, as protests entered a fourth day on Sunday.
Protesters have attacked banks and government buildings and burned police vehicles.
The government has threatened a crackdown, and blames outside forces for the unrest.
Two demonstrators were shot dead in the western town of Dorud on Saturday night. The deputy governor of Lorestan province blamed foreign agents for the deaths.
"No shots were fired by the police and security forces. We have found evidence of enemies of the revolution, Takfiri groups and foreign agents in this clash," Habibollah Khojastehpour said on state television. Iran uses the word Takfiri to describes groups like Daesh.
On Sunday, the semi-official ILNA news agency reported that authorities have arrested some 80 protesters in the city of Arak, some 280 kilometres (173 miles) south of Tehran.
Another official said that 200 people were arrested in Tehran during protests on Saturday.
The government restricted access to the popular photo sharing and messaging apps Instagram and Telegram on mobile phones in a bid to head off further protests.
Police in Tehran fired water cannon to try to disperse demonstrators gathering in Ferdowsi Square in the centre of the capital, according to video footage posted on social media.
Video posted online also showed a clash between protesters and police in the city of Khoramdareh in Zanjan province in the country's northwest. There were also reports of protests in Sanandaj and Kermanshah cities in western Iran.
The videos could not be independently verified.
Calls for Khamenei to step down
The protests which began in the city of Mashhad on Thursday as an attack on high prices, corruption and mismanagement, quickly turned against the government as a whole.
Unemployment stood at 12.4 percent in this fiscal year, up 1.4 percent from the previous year. About 3.2 million Iranians are jobless, out of a total population of 80 million.
The protestors also begun to call on Supreme Leader Ayatollah Ali Khamenei to step down.
The demonstrators also shouted, "Reza Shah, bless your soul".
Such calls are evidence of a deep level of anger and break a taboo. The king ruled Iran from 1925 to 1941 and his West-backed Pahlavi dynasty was overthrown in a revolution in 1979 by Ayatollah Ruhollah Khomeini, the Islamic Republic's first leader.
President Hassan Rouhani said on Sunday Iranians had the right to protest and criticise the government but their actions should not lead to violence or damage public property.
Giving his first public reaction to four days of anti-government demonstrations, Rouhani was quoted by Mehr news agency as telling his cabinet, "Iranians understand the sensitive situation of Iranand region and will act based on their national interests."
Rouhani rebuffed US President Donald Trump's comments in support of the protests and said "those who called Iranians terrorists have no business sympathising with our nation."
The demonstrations are particularly troublesome for Rouhani's government because he was elected on a promise to guarantee rights to freedom of expression and assembly.
Tens of thousands of people also staged demonstrations in support of the government in several cities.
The United States and Canada have thrown their weight behind the protestors.
The latest protests are the biggest since 2009 when mass demonstrations were held after a disputed presidential election.