It said two people were killed and six wounded.
The protests have swept across the country ever since a crowd in the northeastern city of Mashhad took to the streets over the rising cost of living.
Mr Rouhani acknowledged grievances over Iran's economic situation, a lack of transparency and corruption but defended his record. By effectively limiting its citizens' free speech, the Iranian government indicates that it will not loosen its grip and control any time soon.
In the biggest challenge to Tehran since 2009, protests across the country continued for a third day.
How have the authorities responded?
Khojastehpour said: "In these clashes, no bullets were fired by the police, military or security forces towards the people". Mehr also reported that two protesters died in Dorud on Saturday.
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The two were killed in the southwestern city of Izeh, the area's local member of parliament, Hedayatollah Khademi said.
More: Iran unrest threatens Tehran's tyrants.
The IRGC is a powerful force with ties to the country's supreme leader, and is dedicated to preserving the country's Islamic system. These protests are nowhere near as large as the ones in 2009, but they are spreading day by day.
Tehran prosecutor Abbas Jafari Dolatabadi on December 31, admitted that a number of Iranian protesters have been arrested and they would face heavy punishment.
Pavel Durov, the chief executive officer of Telegram, said on Twitter that Iran was "blocking access for the majority of Iranians" after protesters had been using the popular messaging applications in a bid to publicise the demonstrations on social media.
State media have now begun broadcasting some footage on the protests, though it focused on young men attacking banks and vehicles or burning the Iranian flag, reported AFP news agency. Small crowds have gathered in Tehran and police have used water cannon to disperse protesters at a major intersection - as captured in a video obtained by BBC Persian.