"Iranian Patriots, KEEP PROTESTING - TAKE OVER YOUR INSTITUTIONS!!!... HELP IS ON ITS WAY," Trump said in a post on Truth Social, without saying what that help might be.
He said he had cancelled all meetings with Iranian officials until the "senseless killing" of protesters stopped and in a later speech told Iranians to "save the name of the killers and the abusers ... because they'll pay a very big price."
An Iranian official said about 2000 people had been killed in the protests, the first time authorities have given an overall death toll from more than two weeks of nationwide unrest.
US-based rights group HRANA said that of the 2003 people whose deaths it had confirmed, 1850 were protesters. It said 16,784 people had been detained, a sharp increase from the figure it gave on Monday.
Asked what he meant by "help is on its way", Trump told reporters they would have to figure that out.
On Monday evening, Trump announced 25% import tariffs on products from any country doing business with Iran - a major oil exporter. Trump has also said more military action is among options he is weighing to punish Iran over the crackdown.
The US State Department on Tuesday urged American citizens to leave Iran now including by land through Turkey or Armenia.
TRUMP WARNS AGAINST ANY EXECUTIONS
In an interview with CBS News on Tuesday, Trump vowed "very strong action" if the Iranian government started hanging protesters, but again did not elaborate.
"I haven't heard about the hanging. If they hang them, you're going to see some things... We will take very strong action if they do such a thing," Trump said.
According to the Norway-based Iran Human Rights Society, hangings are common in Iranian prisons.
Hengaw, an Iranian Kurdish rights group, has reported that a 26-year-old man, Erfan Soltani, arrested in connection with protests in the city of Karaj, will be executed on Wednesday. Authorities had told the family that the death sentence was final, Hengaw reported, citing a source close to the family.
Reuters could not independently confirm the report and state media has not reported any death sentences so far.
Communications restrictions including an internet blackout have hampered the flow of information in Iran. The UN said phone service had been restored but the internet still faced restrictions.
Trump said on Sunday he planned to speak with billionaire Elon Musk about restoring the internet. Holistic Resilience, a US organisation that works to expand information access in repressive or closed societies, said on Tuesday Musk's Starlink satellite internet service was now available for free in Iran.
The unrest, sparked by dire economic conditions, has posed the biggest internal challenge to Iran's rulers for at least three years and has come at a time of intensifying international pressure after Israeli and US strikes last year.
Iranian security chief Ali Larijani said on X that Trump and Israeli Prime Minister Benjamin Netanyahu were the "main killers" of the Iranian people.
Tehran has not yet responded publicly to Trump's tariff announcement, but it was swiftly criticised by China. Iran, already under heavy US sanctions, exports much of its oil to China, with Turkey, Iraq, the United Arab Emirates and India among its other top trading partners.
Iran's Foreign Minister Abbas Araqchi said on Monday he had continued to communicate with US special envoy Steve Witkoff and that Tehran was studying ideas proposed by Washington.
Witkoff met Reza Pahlavi, the exiled son of Iran's last shah and a prominent voice in the fragmented opposition, over the weekend, Axios reported. Pahlavi has urged Trump to intervene.
Iranian authorities have accused the US and Israel of fomenting the unrest.
Russia on Tuesday condemned what it described as "subversive external interference" in Iran's internal politics, saying any repeat of last year's US strikes would have "disastrous consequences" for the Middle East and international security.
NO SIGNS OF FRACTURE
The protests began on December 28 over the fall in value of the currency and have grown into wider demonstrations and calls for the fall of the clerical establishment.
Despite the protests, the economic strains, and years of external pressure, there are as yet no signs of fracture in the security elite that could bring down the clerical system in power since a 1979 Islamic Revolution.
Iran's authorities have taken a dual approach, cracking down while also calling protests over economic problems legitimate.
Britain, France, Germany and Italy all summoned Iranian ambassadors in protest over the crackdown.
"The rising number of casualties in Iran is horrifying," European Commission President Ursula von der Leyen posted on X.
Underscoring international uncertainty over what comes next in Iran, which has been one of the dominant powers across the Middle East for decades, German Chancellor Friedrich Merz said he believed the government would fall.
"I assume that we are now witnessing the final days and weeks of this regime," he said, adding that if it had to maintain power through violence, "it is effectively at its end".
