In a tweet on Friday, Trump said the Iranian government should "respect their people's rights, including right to express themselves". The semi-official ILNA news agency reported Sunday that authorities had arrested some 80 protesters in the city of Arak, some 175 miles south of Tehran, as well as another 200 in Tehran on Saturday night.
Rouhani's main achievement, a 2015 deal with world powers that curbed Iran's nuclear program in return for a lifting of most global sanctions, is yet to bring the economic benefits the government promised.
Telegram's CEO previously said the app had been blocked for the majority of Iranians.
Protesters in Tehran and elsewhere have called for the resignation of Iran's supreme leader, Ayatollah Ali Khamenei, as witnesses have described crowds chanting "Death to the dictator" and "Clerics should get lost".
In one of the few official reports, an official in Arak, around 300 kilometres (190 miles) southwest of Tehran, said 80 people had been arrested overnight.
Travel restrictions have made it hard to confirm reports about the protests and postings on social media.
Iranian President Hassan Rouhani has made his first speech since widespread protests began in the Islamic Republic.
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.
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The protests have been the biggest show of dissent since huge rallies in 2009.
"Those who misused cyberspace and spread violence are absolutely known to us and we will definitely confront them", Iranian Interior Minister Abdolreza Rahmani Fazli said on state television.
Violence flared in many places on Saturday, and videos posted online suggest demonstrations have continued in a dozen or more cities on Sunday.
There were outbreaks of clashes in several cities on Saturday and two protesters died of gunshot wounds in the western city of Dorud.
Since the 2009 protests against a disputed presidential election that gave hardliner Mahmoud Ahmadinejad a second term were ruthlessly put down, many middle-class Iranians have abandoned hope of securing change from the streets.
The authorities said security forces did not open fire on demonstrators, and blamed the deaths instead on Sunni Muslim extremists and foreign powers.
The protests have erupted at a time of deepening strains between Iran and the administration of U.S. President Donald Trump, who has imposed additional sanctions on Tehran and has threatened to scuttle the nuclear accord. "Looks like they will not take it any longer", Trump wrote. And he adds: "The USA is watching very closely for human rights violations!"
Rouhani criticized Trump in comments aired Sunday night.