The tweet later appeared on President Donald Trump's Twitter account.
The US State Department urged all nations "to publicly support the Iranian people and their demands for basic rights and an end to corruption".
What is Iran saying about the protests?
First Vice-President Eshaq Jahangiri has suggested that government opponents are behind the protests, according to comments reported by state broadcaster IRIB.
He said: "Some incidents in the country these days are on the pretext of economic problems, but it seems there is something else behind them. They think by doing this they harm the government, but it will be others who ride the wave."
Earlier, Fars news agency reported that protesters in Kermanshah had destroyed some public property and were dispersed.
The governor-general of Tehran said that any such gatherings would be firmly dealt with by the police, who are out in force on the main roads.
People there took to the streets to express anger at the government over high prices, and vented their fury against President Hassan Rouhani. Fifty-two people were arrested for chanting "harsh slogans".
The protests spread to other cities on Friday, with thousands turning out in Kermanshah, Rasht, Isfahan and Qom. In Tehran, social media footage showed a heavy police presence.
Some developed into broader demonstrations against the authorities, calling for the release of political prisoners and an end to police beatings.
It was the biggest display of public dissent since huge pro-reform rallies in 2009.
What is behind the unrest?
The protests were initially against economic conditions and corruption but appear to have turned political.
Slogans have been chanted against not just Mr Rouhani but Supreme Leader Ayatollah Ali Khamenei, and clerical rule in general.
Demonstrators were reportedly heard yelling slogans like "The people are begging, the clerics act like God". Protests have even been held in Qom, a holy city home to powerful clerics.
There is also anger at Iran's interventions abroad. In Mashhad, some chanted "not Gaza, not Lebanon, my life for Iran", a reference to what protesters say is the administration's focus on foreign rather than domestic issues.