Protests have rocked the Islamic Republic for almost a week, leaving at least 21 people dead.
Trump wasted no time in blasting the Iranian government on Twitter.
Late on Wednesday, senior Trump administration officials acknowledged their surprise that the protests took hold so quickly.
An 11-year-old boy and a 20-year-old man were reported killed in the town of Khomeinishahr. However, they have said protest rallies are different from vandalism and violent actions.
Calls made across the country for an end to economic hardship and alleged corruption are especially sensitive because Iranian leaders often portray the 1979 Islamic revolution which overthrew the US -backed Shah as a revolt by the poor against exploitation and oppression. "The Iranian government is being tested by its own citizens", she says in a statement.
The government's main challenge is to find a way to suppress the protests without provoking more anger as demonstrators attack police stations, banks and mosques.
Founded in 1981, the NCRI represents political figures, academicians, and other Iranians who have fled their homeland, are dedicated to the overthrow of the Islamic Republic and its replacement with a secular democracy.
IRANIAN AMBASSADOR TO THE UNITED NATIONS GHOLAMALI KHOSHROO, in a letter to the U.N. secretary-general: "Against the backdrop of continuous attempts by previous US administrations to disrupt the course of normal political, social and cultural life in Iran in the past decades, starting with the coup against Iran's democratically elected prime minister in 1953, the current USA administration has crossed every limit in flouting rules and principles of global law governing the civilized conduct of worldwide relations". Rather, like citizens in many places around the world, especially countries with oil, some Iranians are asking why they should make such sacrifices for a government that lacks accountability and is excessively corrupt.
Views in the United States, and among Iranians everywhere, range from exuberant embrace of every tweet to disgusted dismissal of them all. Ambassador Gholamali Khoshroo says USA leaders have "incited Iranians to engage in disruptive acts" and the US government has been intervening "in a grotesque way in Iran's internal affairs". He called for "thorough, independent and impartial investigations of all acts of violence".
US President Donald Trump continued to tweet on the protests despite criticism from many Iran experts that his comments are counterproductive. Rouhani's office did not mention the comment.
"Today we can announce the end of the 2018 sedition", Mohammad Ali Jafari, commander of the Revolutionary Guards, said on its website, adding that the number of protesters "did not exceed 15,000 people nationwide".
It remains hard for journalists to piece together what's happening beyond the capital, especially as the government has blocked both the photo-sharing app Instagram and the messaging app Telegram, which protesters have used to organize their demonstrations and share footage. Many shared notices about upcoming rallies and videos documenting the protests, until the authorities shut it down to "maintain peace".
The head of Tehran's Revolutionary Court, Musa Ghazanfarabadi, said protesters would be tried soon and the ringleaders could be charged with "moharebeh" - an Islamic term meaning warring against God - which carries the death penalty. A gunshot and muzzle flash could be seen in the footage taken in Isfahan province, where there have been days of protests. That view seems to lend credence to commentary that Iran's hardliners themselves started the protests initially to weaken reformers by highlighting the failure of the nuclear deal to bring about tangible economic benefits. Several protest leaders eventually were sentenced to death.