The Foreign Ministry in Tehran dismissed Trump's comments, saying "the Iranian people place no value or credibility in the opportunistic claims of US officials or of Mr. Trump himself".
Some videos showed protesters chanting "Death to the dictator!" and "Death to [Iranian President Hassan] Rouhani".
Telegram is particularly popular in Iran.
Rouhani and other leaders made a point to warn that the government wouldn't hesitate to crack down on those it considers lawbreakers amid the demonstrations, which began Thursday over the economic woes plaguing Iran.
Iranian media also reported the disruption.
Overnight unrest in the capital Tehran was concentrated in a few major intersections, according to the semi-official Tasnim news agency.
There were outbreaks of clashes in several cities on Saturday and two protesters died of gunshot wounds in the western city of Dorud.
The unauthorized protests have challenged authorities, with crowds turning revolutionary slogans against the government of the Islamic Republic, which took power after a revolution in 1979.
The largest protests to strike Iran in almost a decade continued unabated Sunday, despite a government move to block access to Instagram and a popular messaging app used by activists to organize, with even President Hassan Rouhani acknowledging the public's anger over the Islamic Republic's flagging economy.
Iranian Communications Minister Mohammad-Javad Azari Jahromi had earlier accused channels like Amadnews of promoting "armed uprising and social unrest".
The local authorities added, however, that the security forces had not opened fire at protesters.
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.
US President Donald Trump weighed in on the protests, saying "oppressive regimes can not endure forever".
The Canadian government has expressed support for people protesting in Iran on Monday as mass demonstrations enter their fifth day across the country. "Looks like they will not take it any longer", Trump wrote.
Rouhani criticized Trump in comments aired Sunday night.
"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.
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