Iran's Supreme Leader Ayatollah Ali Khamenei on Saturday blamed US President Donald Trump for weeks of demonstrations that rights groups said have led to more than 3,000 deaths.

"We consider the US president criminal for the casualties, damages and slander he inflicted on the Iranian nation," Khamenei said, according to Iranian state media.

The protests erupted on December 28 over economic hardship and swelled into widespread demonstrations calling for the end of clerical rule in the Islamic Republic.

Trump has repeatedly threatened to intervene, including by threatening "very strong action" if Iran executed protesters.

But on Friday, in a social media post, he thanked Tehran's leaders, saying they had called off mass hangings. Iran said there was "no plan to hang people".

In comments that appeared to respond to Trump, Khamenei said: "We will not drag the country into war, but we will not let domestic or international criminals go unpunished," state media reported.

In an interview with Politico on Saturday, Trump said “it’s time to look for new leadership in Iran” and called for an end to Khamenei’s 37-year rule.

In a separate interview with Reuters on Wednesday, Trump said that Iranian opposition figure Reza Pahlavi “seems very nice,” but ⁠expressed uncertainty over whether Pahlavi would be able to muster support within Iran to eventually take over.

Iran's ultimate authority Khamenei said "several thousand deaths" had happened during the nationwide protests, which are Iran's worst unrest in years. He accused Iran's longtime enemies the US and Israel of organising the violence.

"Those linked to Israel and the US caused massive damage and killed several thousand," he said, adding that they started fires, destroyed public property and incited chaos. They "committed crimes and a grave slander," he said.

The US-based Human Rights Activists News Agency, or HRANA, said it had verified 3,090 deaths, including 2,885 protesters, and over 22,000 arrests. These figures have not been independently verified.

Last week, Iran's prosecutor general said detainees would face severe punishment.

Those held included people who "aided rioters and terrorists attacking security forces and public property" and "mercenaries who took up arms and spread fear among citizens," he said.

"All perpetrators are mohareb," state media quoted Mohammad Movahedi Azad as saying, adding that investigations would be conducted "without leniency, mercy or tolerance".

Mohareb, an Islamic legal term meaning to wage war against God, is punishable by death under Iranian law.

State media has reported the arrest of thousands of "rioters and terrorists" across the country, including people linked to opposition groups abroad that advocate the overthrow of the Islamic Republic. (Reuters)