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.
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.
The protesters have been chanting slogans, criticizing Rouhani and Iran's Supreme Leader Ali Khamenei.
The Iranian president also acknowledged the public's worries extend beyond economy to corruption allegations and government transparency.
A semi-official news agency in Iran is reporting that police arrested around 200 people during protests in Tehran on Saturday.
Government officials have said the protests are part of a wider attempt by Rouhani's opponents to discredit his leadership. "The people are finally getting wise as to how their money and wealth is being stolen and squandered on terrorism".
Trump responded to the protests with a tweet saying, "Many reports of peaceful protests by Iranian citizens fed up with regime's corruption & its squandering of the nation's wealth to fund terrorism overseas. The USA is watching very closely for human rights violations!"
"Iranian authorities are blocking access to Telegram for the majority of Iranians after our public refusal to shut down. peacefully protesting channels", he wrote.
State TV's website reported the decision Sunday, citing an anonymous source who said it was "in line with maintaining peace and security of the citizens". The Telegraph has changed her first name for security reasons.
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The ship, loaded with the Japanese refined petroleum, was claimed to be heading to Taiwan. The statement did not address whether or not Russian ships had transferred the fuel.
Telegram is particularly popular in Iran.
Facebook, which owns Instagram, did not immediately respond to a request for comment.
CEO Pavel Durov made the announcement on Twitter Sunday.
"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.
Facebook itself has been banned in Iran since the 2009 protests that followed the re-election of hard-line President Mahmoud Ahmadinejad.
Users said Sunday that they could no longer access the app via cellphone networks, though it was still available via Wifi and home internet connections.
And when that happened, state media was also forced to acknowledge that it had not initially reported on the protests on the orders of security officials.
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.
Earlier on Sunday, authorities of the country's western Lorestan province confirmed that two people had died during the protests in the province.