At least five people have been killed in the unrest, which began on Friday after the announcement of fuel rationing and a 50% hike in the price of petrol.
At least 100 banks, buildings and cars were torched, according to state media.
Iranian authorities shut down the internet on Saturday but videos shared online before then contained sounds of gunfire and images of badly injured people.
In a statement, the country's main security force said: "If necessary we will take decisive and revolutionary action against any continued moves to disturb the people's peace and security."
Fars, a semi-official news agency in Iran, said there had been more than 87,000 protesters across the country and that around 1,000 had been arrested.
The streets were reportedly calmer on Monday and General Gholamreza Soleimani, head of the Basij, Iran's paramilitary Revolutionary Guard, insisted security forces had acted with "restraint and patience".
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