The US President's latest intervention, via Twitter, was released as news agencies reported that two protesters had apparently been shot dead by security forces in the western Iranian town of Dorud.
There was no independent verification of video, said to show the bodies, that was circulating on social media.
Disruption to the internet and mobile phone services was also reported in some areas.
There is a growing security presence in Iran's major cities and towns
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There is understood to be increased security in many of Iran's major cities and towns
President Trump released a series of tweets on Saturday as the protests became more widespread.
On Saturday evening, he said: "The entire world understands that the good people of Iran want change, and, other than the vast military power of the United States, that Iran's people are what their leaders fear the most."
"Oppressive regimes cannot endure forever, and the day will come when the Iranian people will face a choice. The world is watching!"
Speaking on state television on Sunday, Iranian interior minister Abdolrahman Rahmani Fazli warned protesters: "Those who damage public property, disrupt order and break the law must be responsible for their behaviour and pay the price".
The protests began when hundreds of people took to the streets in Mashhad, Iran's second-largest city and one of the holiest places in Shia Islam, on Thursday.
Pro-regime rallies in Iran
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Rival marchers carried banners supporting Supreme Leader Ayatollah Ali Khamenei
They spread to Tehran and other cities on Friday, with police using water cannon in some cases to disperse the crowds.
Initially aimed against high prices, the anti-government protests quickly turned against the Islamic regime as a whole.
Police arrested 52 people.
On Saturday, tens of thousands of government supporters marched in cities across Iran in a show of support for the regime.
Many reports of peaceful protests by Iranian citizens fed up with regime’s corruption & its squandering of the nation’s wealth to fund terrorism abroad. Iranian govt should respect their people’s rights, including right to express themselves. The world is watching! #IranProtests
— Donald J. Trump (@realDonaldTrump) December 30, 2017
Many of the marchers carried banners backing Supreme Leader Ayatollah Ali Khamenei.
Small anti-government protests were continuing around the University of Tehran - where tear gas appeared to have been fired.
Mr Trump tweeted earlier on Saturday: "Many reports of peaceful protests by Iranian citizens fed up with regime's corruption and its squandering of the nation's wealth to fund terrorism abroad.
"Iranian govt should respect their people's rights, including right to express themselves. The world is watching!"
Iranian students scuffle with police at the University of Tehran
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Iranian students faced off against police at the University of Tehran
The US State Department condemned the arrest of peaceful protesters and urged "all nations to publicly support the Iranian people and their demands for basic rights and an end to corruption".
Iran's foreign ministry spokesman, Bahram Ghasemi, dismissed the comments coming from Washington, saying that "Iranian people give no credit to the deceitful and opportunist remarks of US officials or Mr Trump."
The US President has refused to re-certify a 2015 deal between Tehran and world powers that curbed Iran's disputed nuclear programme in return for a lifting of most international sanctions.
The deal was one of the biggest achievements by President Hassan Rouhani, but has yet to bring the broad economic benefits.
State television said pro-government rallies were scheduled to be held in more than 1,200 cities and towns on Saturday
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The government-sanctioned rallies have been held annually to mark the end of protests surrounding Iran's disputed 2009 presidential election.
Protesters at the time said the vote, which marked Mahmoud Ahmadinejad's re-election as president, was rigged, and tens of thousands of people staged street protests for eight months.
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