Tehran (AFP) - Reports of clashes and marches spread across Iran on Saturday as protests spilled into a third night despite government warnings against any further "illegal gatherings".

Unverified videos on social media appeared to show thousands marching through the western cities of Khorramabad, Zanjan and Ahvaz and many smaller towns, while reports spread rapidly that several people had been shot dead by police in the town of Dorud.

A swirl of wild rumours, combined with travel restrictions and a near-total media blackout from official agencies, made it difficult to confirm the reports.

The authorities appeared to respond by temporarily cutting internet access to mobile phones, but full coverage was eventually restored.

Several Iranian news agencies warned Telegram, the most popular social media service in the country, might soon be shut down after communications minister Mohammad-Javad Azari Jahromi accused one channel, Amadnews, of encouraging an "armed uprising".

One of the few official reports -- by conservative Mehr news agency -- showed protesters attacking a town hall in central Tehran, overturning a police car and burning the Iranian flag.

There was chaos earlier around the capital's university as hundreds took to the streets, blocking traffic and shouting slogans against the regime.

But the authorities could also count on a show of strength, with hundreds of counter-demonstrators seizing control of the university entrance, chanting "Death to the seditionists".

Annual rallies marking the defeat of the last major protest movement in 2009 had already been scheduled for Saturday morning and brought thousands of regime supporters to the streets across the country.

"We urge all those who receive these calls to protest not to participate in these illegal gatherings as they will create problems for themselves and other citizens," said Interior Minister Abdolrahman Rahmani Fazli.

- 'A new plot' -

The protests began in the second city of Mashhad on Thursday as an attack on high living costs but quickly turned against the Islamic regime as a whole.

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There were even chants in favour of the monarchy toppled by the Islamic revolution of 1979, while others criticised the regime for supporting the Palestinians and other regional movements rather than focusing on problems at home.

State news channel IRINN said it had been banned from covering the protests that spread to towns and cities including Qom and Kermanshah.

"The enemy wants once again to create a new plot and use social media and economic issues to foment a new sedition," Ayatollah Mohsen Araki, a prominent cleric, told a crowd in Tehran, according to the conservative Fars news agency.

Other officials also pointed the blame outside Iran.

"Although people have a right to protest, protesters must know how they are being directed," Massoumeh Ebtekar, vice president in charge of women's affairs, wrote on Twitter.

She posted images from Twitter accounts based in the United States and Saudi Arabia, voicing support for the Mashhad protests.

US President Donald Trump tweeted later that Iran's people wanted change and "oppressive regimes cannot endure forever".

"The day will come when the Iranian people will face a choice," he wrote, his second time addressing the subject in as many days. "The world is watching!"

White House Press Secretary Sarah Sanders added: "The days of America looking the other way from the Iranian regime's oppression are over. America stands with the Iranian people."

Trump's tweets on Friday prompted Iran's foreign ministry spokesman Bahran Ghasemi to dismiss his remarks as "opportunistic".

- 'Serious challenges' -

Iranian officials warned against dismissing the public anger seen in recent days.

"The country is facing serious challenges with unemployment, high prices, corruption, lack of water, social gap, unbalanced distribution of budget," tweeted Hesamoddin Ashena, cultural adviser to President Hassan Rouhani.

"People have the right for their voice to be heard."

There has been particular anger at welfare cuts and fuel price increases in the latest budget announced earlier this month.

Since the 2009 protests were ruthlessly put down by the Revolutionary Guards, many middle-class Iranians have abandoned hope of pressing for change from the streets.

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

Some of this week's protests were directed against financial scandals linked to unauthorised lending institutions which collapsed with the loss of hundreds of thousands of accounts.

Payam Parhiz, editor-in-chief of reformist media network Nazar that broke the news of the Mashhad protests, said they were more focused on the economy than those in 2009, which were sparked by allegations of election-rigging.

"Then, they were middle-class and their slogans went beyond economic matters to things like cultural liberties," he told AFP.

"Today, the concerns are economic. There are people who have lost their life savings. They will protest until their problems are resolved."

Since taking power in 2013, Rouhani has sought to clean up the banking sector and kick-start the economy, but many say progress has been too slow.

Aware that economic problems can quickly spiral into political chaos, officials from across the political spectrum have called for greater efforts to tackle poverty and the 12 percent unemployment rate.

"Solving people's economic problems is the chief priority in the country," tweeted Ebrahim Raisi, the hardline cleric defeated by Rouhani in May's presidential election.