Demonstrators took the streets for a fifth straight day of marches that have broken out in cities across the country. "Our economy needs an operation".
Police in a dozen cities were reported to have shot at protesters, possibly causing further deaths. Unemployment in the spring of 2017 was 12.6 percent, up slightly from late 2016, according to the World Bank.
The Intelligence Ministry said in a statement that "rioters and instigators" had been identified "and will be dealt with seriously soon".
That was echoed Monday by judiciary chief Ayatollah Sadegh Larijani, who urged authorities to confront rioters, state TV reported.
The Iranian government shut down access to social media platform Instagram on Sunday, as well as a popular messaging app, which protesters used to organize.
Police used tear gas and water cannons to disperse a small protest in Tehran's Enghelab Square on Sunday evening, according to unverified social media videos.
"Certainly, the great Iranian nation has closely pursued Mr. Trump's active partnership in violating the Palestinian, Yemeni and Bahraini people's human rights" and remember his hostile approach towards Iranians' visit to the USA, he added. "They're also demanding more freedoms", said Rowhani, in an indirect attack on regime hardliners who oppose his attempts to push through political and cultural reforms.
US President Donald Trump, who has been tweeting in support of the protesters, continued into the New Year, describing Iran as 'failing at every level despite the bad deal made with them by the Obama Administration'.
Iranian President Hassan Rouhani said Iranians had the right to criticize authorities but also warned of a crackdown.
The Russian Foreign Ministry said on January 1 that the unrest was "Iran's internal affair", adding that any "external interference destabilizing the situation is inadmissible".
Pointing to a humiliating defeat that enemies suffered in their recent attempts to hijack the peaceful rallies in Iran, the general said the evil American and Zionist plots against the Islamic Republic have been hatched while the U.S. itself saw various public protests against Washington's policies and measures in 2017.
British Foreign Secretary Boris Johnson called for a meaningful debate about the protesters' issues and said on Facebook that "the United Kingdom is watching events in Iran closely".
Israeli Prime Minister Benjamin Netanyahu praised the "brave Iranians" protesting against a regime that "wastes tens of billions of dollars spreading hate".
He also called on "all concerned to refrain from violence and for global obligations on human rights to be observed".
"This is nothing", Mr Rouhani said. "They have nothing to be happy about", said Sarita Mohammadi, a 35-year-old teacher in Tehran.
"This man who today in America wants to sympathise with our people has forgotten that a few months ago he called the nation of Iran terrorist".