The US President said "all of the money that President Obama so foolishly gave them went into terrorism and into their 'pockets,"' referring to the global deal that removed some economic sanctions on Iran in exchange for curbs on its nuclear program.
Mr Trump opposes the deal.
"The people of Iran are finally acting against the brutal and corrupt Iranian regime," his tweet also said.
"The people have little food, big inflation and no human rights. The US is watching!"
Iran is currently the largest demonstrations since its disputed 2009 presidential election.
Six days of unrest have seen at least 20 people killed and around 450 protesters arrested in the capital of Tehran.
Offering his first comments since they began, Supreme Leader accused the "enemies of Iran" of meddling in the country's affairs.
Ayatollah Ali Khamenei said: "In recent days, enemies of Iran used different tools including cash, weapons, politics and intelligence apparatus to create troubles for the Islamic Republic."
He did not mention any enemies by name but Ali Shamkhani, secretary of the Supreme National Security Council, said the United States, Britain and Saudi Arabia were behind the recent riots.
"Saudis will receive Iran's unexpected response and they know how serious it can be," Mr Shamkhani was quoted as saying by Tasnim news in an interview with Beirut-based Al Mayadeen TV.
In an earlier tweet, Mr Trump supported the protesters, writing: "The great Iranian people have been repressed for many years. They are hungry for food and for freedom.
"Along with human rights, the wealth of Iran is being looted. TIME FOR CHANGE!"
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