At least 21 people have died as demonstrators clashed with security forces in cities and towns across the country.
Hundreds have been arrested over the last few days and a number of public buildings have been damaged or gutted by fire.
Mr Trump said on Twitter: "The people of Iran are finally acting against the brutal and corrupt Iranian regime," Trump tweeted, a day after calling for regime change in the Islamic republic.
"All of the money that President Obama so foolishly gave them went into terrorism and into their 'pockets.' The people have little food, big inflation and no human rights. The US is watching!"
State TV said six rioters were killed in the town of Qahderijan, during an attack on a police station. The clashes were sparked off as protesters tried to steal guns, according to the reports.
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Two people, a 20-year-old man and a boy aged 11, died in the town of Khomeinishahr and a member of the Revolutionary Guards was killed in nearby Kahriz Sang.
Iran's Supreme Leader Ayatollah Ali Khamenei, making his first public statement on the violence, claimed "enemies of Iran" had stirred up unrest using "cash, weapons, politics and intelligence apparatus to create trouble for the Islamic Republic".
Various unverified social media posts from activists, including a number of videos, appeared to show protests from locations across the country.
The head of Tehran's Revolutionary Court reportedly warned protesters they could potentially face the death penalty.
Organisers appear to have used social media to call for more protests in dozens of towns and cities across the country tonight from 5pm local time (1.30pm UK time).
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The demonstrations, the largest to strike Iran since its disputed 2009 presidential election, have been sparked by anger over the country's flagging economy and a jump in food prices.
President Hassan Rouhani called for calm, warning that the government would not tolerate violence.
Turkey, meanwhile, said it was "concerned" protests were "spreading" and called for "common sense" to prevent "any escalation".
The secretary of Iran's Supreme National Security Council, Ali Shamkhani, blamed the UK, the US and Saudi Arabia for fomenting the protests on social media.
Theresa May's spokesman said the UK Government thinks there should be meaningful debate within Iran on the issues being raised by the protesters.
The protests began on Thursday in the northeastern city of Mashhad, Iran's second-largest, and quickly spread across the nation, with some protesters chanting against the government and Ayatollah Khamenei.
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