Donald Trump has threatened Iranian President Hassan Rouhani with "consequences the likes of which few throughout history have ever suffered before" after he spoke out on America's anti-Iran policy.

In an explosive, all-caps tweet Mr Trump told Mr Rouhani to "never, ever threaten the United States again" and told him to "be cautious!".

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The comments come after Mr Rouhani cautioned Mr Trump about pursuing hostile policies against Tehran, saying "America should know … war with Iran is the mother of all wars".

"Mr Trump, don't play with the lion's tail, this would only lead to regret," Mr Roiuhani said on Sunday, according to Iran's state-owned news agency the IRNA.

"You are not in a position to incite the Iranian nation against Iran's security and interests."

Sorry, this video has expired Iranian President Hassan Rouhani warns US President Donald Trump: "don't play with the lion's tail".

IRNA, a Government mouthpiece, promptly dismissed Mr Trump's tweet, describing it as a "passive reaction" to Mr Rouhani's remarks.

It said Mr Trump's Twitter missive was only mimicking and copying Iranian Foreign Minister Mohammad Javad Zarif, who had in the past warned the West to "never threaten an Iranian".

High-ranking Iranian officer General Gholam Hossein Gheibparvar also said Mr Trump's warning of unprecedented "consequences" for Iran, should it threaten the United States, is nothing but "psychological warfare".

General Gheibparvar, the chief of the paramilitary Revolutionary Guard's volunteer Basij force, said Mr Trump "won't dare" take any military action against Iran.

"We will never abandon our revolutionary beliefs ... we will resist pressure from enemies. America wants nothing less than [to] destroy Iran ... [but] Trump cannot do a damn thing against Iran," Iranian Students News Agency ISNA reported General Gheibparvar as saying.

Iranian lawmaker Heshmatollah Falahatpisheh said he doubted it would come to a military confrontation between Iran and the United States, despite the escalating rhetoric.

Iran run by 'something that resembles the mafia': Pompeo

Earlier, US Secretary of State Mike Pompeo launched his own rhetorical assault on Iran's leaders, comparing them to a "mafia" and promising unspecified backing for Iranians unhappy with their Government.

Sorry, this video has expired Mike Pompeo pledges solidarity with Iranians rebelling against regime

Mr Pompeo, in a California speech to a largely Iranian-American audience, dismissed Mr Rouhani and Foreign Minister Javad Zarif, who negotiated a nuclear deal with the United States and five other countries, as "merely polished front men for the ayatollahs' international con artistry".

Iran "is run by something that resembles the mafia more than a government," Mr Pompeo said, citing what he called Iranian leaders' vast wealth and corruption.

In the speech at the Ronald Reagan Presidential Library and Museum, Mr Pompeo also said the Iranian Government had "heartlessly repressed its own people's human rights, dignity and fundamental freedoms".

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Mr Pompeo said despite poor treatment by their leaders, "the proud Iranian people are not staying silent about their Government's many abuses".

"And the United States under President Trump will not stay silent either," he said.

"In light of these protests and 40 years of regime tyranny, I have a message for the people of Iran: The United States hears you. The United States supports you. The United States is with you."

Mr Pompeo's speech was the latest step in a communications offensive launched by the Trump administration that is meant to foster unrest in Iran and help pressure its Government to end its nuclear program and support of militant groups, US officials familiar with the matter said.

Iran reacted to Mr Pompeo's speech by claiming it was an interference in its affairs, the semi-official Tasnim news agency reported.

"Pompeo's speech on Sunday was a clear interference in Iran's state matters … such policies will unite Iranians who will overcome plots against their country," Tasnim quoted Iranian Foreign Ministry spokesman Bahram Qasemi as saying.

The US offensive is meant to work in concert with severe economic sanctions that Washington plans to reimpose in the coming months, including on Tehran's oil exports, its principal revenue generator.

The United States will work with countries that import Iranian oil "to get imports as close to zero as possible" by November 4, Mr Pompeo said.

ABC/wires