Since Thursday, Iran has been rocked by the largest protests over the past years.
The protests have since attracted global attention, and footage of the action has been shared hundreds of thousands of time on social media.
Overnight unrest in the capital Tehran was concentrated in a few major intersections, according to the semi-official Tasnim news agency.
The guard - whose mandate is to safeguard the Islamic Revolution - warned late Saturday that protesters would face an iron hand if demonstrations didn't stop.
Iranian authorities said the majority of social media reports were emanating from regional rival Saudi Arabia and exile groups based in Europe.
Rouhani's main achievement, a 2015 deal with world powers that curbed Iran's nuclear program in return for a lifting of most worldwide sanctions, is yet to bring the economic benefits the government promised.
Two protesters were shot dead in the western town of Dorud on Saturday night.
Activists were using Telegram to organize and discuss the protests, and they also used Instagram to share photos and videos of the demonstrations.
"It has been decided in the highest security level to restrict access to Telegram (messaging app) and Instagram", Iranian state television quoted an informed source as saying.
They are also hard for the government of President Hassan Rouhani because he was elected on a promise to guarantee rights to freedom of expression and assembly.
The Iranian government is denying responsibility for the deaths and unrest..
Violence flared in many places on Saturday, and videos posted online suggest demonstrations have continued in a dozen or more cities on Sunday.
The authorities said security forces did not open fire on demonstrators, and blamed the deaths instead on Sunni Muslim extremists and foreign powers. "Oppressive regimes can not endure forever, and the day will come when the Iranian people will face a choice".
"Big protests in Iran", he later added.
US President Donald Trump weighed in on the protests, saying "oppressive regimes can not endure forever". "Looks like they will not take it any longer", Trump wrote.
"This gentleman in America, who is now trying to sympathise with our nation, appears to have forgotten that he called the Iranian nation terrorists several months ago", he was reported to have said.
"This man, who is an enemy of the Iranian nation from the top of his head to his very toes, has no right to sympathise with Iranians", he added. "We pray that freedom and human rights will carry the day".
Rouhani criticized Trump in comments aired Sunday night.