"Iran has become so unstable that the regime has shut down their entire Internet System so that the Great Iranian people can not talk about the tremendous violence taking place within the country", the USA leader tweeted.
Officials have confirmed five deaths, including of three security personnel stabbed by "rioters".
The International Monetary Fund said it regretted the violence and loss of life and had not discussed the gasoline price hike with Iran.
Amnesty International said it had documented at least 106 protesters killed by security forces, which would make it the worst street unrest in Iran in at least a decade and possibly since the 1979 Islamic Revolution.
Iranian authorities said several people, including members of the security forces and policemen, were killed in street violence, which Tehran blamed on "foreign foes".
Ascertaining information about the unrest has become increasingly hard following a near-total shutdown of the Internet inside Iran.
It comes at a time when Iran's economy has been crippled by US sanctions that have almost halted its exports of oil, and when governments in Lebanon and Iraq that include Iran-backed factions have also faced increasingly violent demonstrations.
Iran's mission to the United Nations called the Amnesty toll "speculative" and said Iran was subject to a "disinformation campaign".
Iran's neighbor Iraq has been hit by weeks of its own anti-government protests, with demonstrators voicing resentment over what they describe as Tehran's meddling in their country.
The New York-based Center for Human Rights in Iran announced Thursday that members of the non-profit Persian Wildlife Heritage Foundation were spending six to ten years in prison for "contact with the 39, U.S. enemy state ". The latter - triggered by the Trump administration after the U.S. unilaterally withdrew from the Iran nuclear deal - have dealt a deadly blow to the Iranian economy, ensuring that Tehran, a petrochemical powerhouse, is unable to sell its oil and gas or access the worldwide financial system.
"We echo the statement on Iran made by the Office of the High Commissioner for Human Rights yesterday, including the call to immediately re-establish Iranian's access to the Internet".
"Our income has not increased at all but costs have tripled or quadrupled", Ehsan, a lawyer, informed AFP.
The web blackout remained largely in impact on Thursday, with Iranians overseas tweeting hashtags like #Internet4Iran and calling for an finish to the outage.
The national security council made the decision to pull the plug on internet access, said semi-official news agency ISNA.