Iran dismissed a US offer to renegotiate a historic 2015 nuclear deal signed with other major powers as President Donald Trump reimposed crippling sanctions on Tuesday.

Trump's withdrawal from the agreement in May has infuriated European partners who were determined to keep it alive and now find their businesses operating in Iran faced with the threat of US legal penalties.

The sanctions that went into effect on Tuesday target Iranian access to US banknotes and key economic sectors including cars and carpets.

Much of the damage has already been done, with Trump's aggressive rhetoric fuelling a run on the rial in recent months, while worsening inflation has stoked public protests against the government's management of the economy that have intensified over the past week.

Most Iranians see US hostility as a basic fact of life, so their frustration is largely directed at their own leaders for not handling the situation better.

“Prices have been increasing for three or four months and everything we need has become so expensive, even before sanctions returned,” said Yasaman, a 31-year-old photographer in Tehran.

He said Iran's leaders may need to “drink the poison cup” and negotiate with the US.

In a statement on Monday just hours before the sanctions went back into force, Trump said: “The Iranian regime faces a choice.

“Either change its threatening, destabilising behaviour and reintegrate with the global economy, or continue down a path of economic isolation.

“I remain open to reaching a more comprehensive deal that addresses the full range of the regime's malign activities, including its ballistic missile programme and its support for terrorism,” Trump said.

But his Iranian counterpart Hassan Rouhani dismissed the idea of talks while crippling sanctions were in force.

“If you're an enemy and you stab the other person with a knife, and then you say you want negotiations, then the first thing you have to do is remove the knife,” he told state television.

“They want to launch psychological warfare against the Iranian nation,” Rouhani said. “Negotiations with sanctions doesn't make sense.”

Rial rally

Iran's currency has lost around half its value since Trump announced the US would withdraw from the nuclear pact.

But the last two days have seen an impressive 20 percent rally in the value of the rial after the government announced new foreign exchange rules and launched a corruption crackdown that included the arrest of the central bank's currency chief.

The new rules allow unlimited tax-free currency and gold imports, and reopen exchange bureaus after a disastrous attempt to fix the value of the rial in April backfired spectacularly with corrupt traders making a fortune out of a mushrooming black market.

Iran is also taking solace in the fact that most of the world strongly opposes Trump's policy, with China, India and Turkey all saying they are unwilling to substantially cut purchases from Iran when the US reimposes sanctions on the energy sector on November 5.

The European Union's diplomatic chief Federica Mogherini said the bloc deeply regrets the US move.

“We are determined to protect European economic operators engaged in legitimate business with Iran,” she said in a statement co-signed by the foreign ministers of Britain, France and Germany.

Iranian Foreign Minister Mohammad Javad Zarif told reporters the global reaction to Trump's move showed that the US was diplomatically “isolated,” but acknowledged the sanctions “may cause some disruption.”

'Severe consequences'

Many large European firms are leaving Iran for fear of US penalties, and Trump warned of “severe consequences” for firms and individuals that continued to do business with Iran.

The US sees the sanctions “as a tool to pressure Iran to come back to the negotiating table to rehash the nuclear deal on terms more to Trump's liking.

That is not going to happen,” said John Glaser of the Cato Institute.

Two countries that have welcomed the tough new US policy are Iran's regional rivals, Israel and Saudi Arabia.

Israeli Prime Minister Benjamin Netanyahu hailed the renewed sanctions as “an important moment for Israel, for the US, for the region, for the whole world.”

There have been rumours that Trump and Rouhani could meet in New York in September on the sidelines of the UN General Assembly — though Rouhani reportedly rejected US overtures for a meeting at last year's event.

There was little word of fresh protests after days of unrest in Mashhad, Isfahan and other major cities — although verifying information remains difficult due to severe reporting restrictions.