Iran will seek dialogue with protest leaders after demonstrations in Tehran and other cities over a plunge in the currency's value that has accelerated inflation, with the central bank chief resigning, the government said on Tuesday.

Protests, which included shopkeepers in Tehran's Grand Bazaar, were held on Sunday and Monday according to Iranian state media, the latest demonstrations in the Islamic Republic where bouts of unrest have repeatedly erupted in recent years.

President Masoud Pezeshkian said in a social media post late on Monday that he had asked the interior minister to listen to "legitimate demands" of protesters.

Government spokeswoman Fatemeh Mohajerani said a dialogue mechanism would be set up and include talks with protest leaders.

"We officially recognise the protests ... We hear their voices and we know that this originates from natural pressure arising from the pressure on people's livelihoods," she said on Tuesday in comments carried by state media.

The Iranian rial has been falling as the economy has suffered from the impact of Western sanctions, sinking to a record low on Monday at around 1,390,000 to the U.S. dollar, according to websites monitoring open market rates.

"We have fundamental measures on the agenda to reform the monetary and banking system and maintain the purchasing power of the people," Pezeshkian posted on X.

Iranian media have said the government's recent economic liberalisation policies have put pressure on the open-rate rial market, where ordinary Iranians buy foreign currency.

In 2022, Iran was buffeted by protests across the country over price hikes, including for bread, a major staple.

Over the same period and into 2023, the country's clerical rulers faced the boldest unrest in years touched off by the death of a young Iranian Kurdish woman, Mahsa Amini, in the custody of the morality police, who enforce strict dress codes.

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