The protests erupted over falling living standards.
However, a Revolutionary Guards commander said the protests had degenerated into people chanting political slogans and burning public property.
The recent protests are the biggest show of dissent since huge pro-reform rallies in 2009. There are reports of two deaths.
In the cities of Khoramabad, Zanjan and Ahvaz there were calls for the removal or death of Iran’s Supreme leader, Ayatollah Ali Khamenei.
Iran’s Islamic Revolutions Guards Corp is a powerful force with ties to the country’s supreme leader, and is dedicated to preserving the country’s Islamic system.
Brigadier-General Esmail Kowsari told the ISNA news agency: “If people came into the streets over high prices, they should not have chanted those slogans and burned public property and cars.”
The interior minister has also warned the public that protesters will be held accountable.
Protests began in the north-eastern city of Mashhad on December 28 and spread to other major cities on December 29.
A small demonstration in the capital Tehran grew to several thousand people on December 30, and students clashed with police. The protests also became violent in several other towns.
Iran is a key provider of military support to the government of Bashar al-Assad in Syria. It is also accused of providing arms to Houthi rebels fighting a Saudi-led coalition in Yemen, which it denies, and is an ally of Lebanon’s powerful Shia movement Hezbollah.
The Iranian authorities are blaming anti-revolutionaries and agents of foreign powers for the outbreak.
Also on December 30, thousands of pro-government demonstrators turned out for pre-arranged rallies to mark the eighth anniversary of the suppression of the 2009 street protests.
The US has led international support for the protesters.
President Donald Trump tweeted: “Oppressive regimes cannot endure forever, and the day will come when the Iranian people will face a choice. The world is watching!”
Iran’s foreign ministry called earlier comments from President Trump and other US officials “opportunistic and deceitful”.
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