The European Union's foreign affairs chief has said that the union regrets the reintroduction of economic sanctions against Iran by the United States.

Federica Mogherini said the EU was "determined to protect European economic operators engaged in legitimate business with Iran."

The reintroduction of the sanctions bring back into effect harsh penalties that had been lifted under a historic, multi-party nuclear agreement that US President Donald Trump abandoned in May.

Mr Trump said the new measures were the "most biting sanctions ever imposed".

He tweeted: "In November they ratchet up to yet another level. Anyone doing business with Iran will NOT be doing business with the United States. I am asking for WORLD PEACE, nothing less!"

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

Speaking in New Zealand, Ms Mogherini said the EU had moved to protect industries who had already invested in Iran under the terms of the 2015 nuclear deal. 

She said: "There is also a matter of trade sovereignty to be protected.

"This Blocking Statute has now been updated, so the legislation in Europe protects European businesses from the effects of the US sanctions."

The first of two rounds of US sanctions target Iran's access to US banknotes and key industries, including cars and carpets.

Iranians are already seeing the effects of the sanctions, with Iran's rial currency losing around half its value since Mr Trump announced the US would withdraw from the 2015 nuclear accord.

Mr Trump's contempt for the nuclear deal dates back to his time as presidential candidate. On 8 May, he made good on a pledge to pull the US out of the international agreement.

He blasted the agreement yet again yesterday, calling it a "horrible, one-sided deal (that) failed to achieve the fundamental objective of blocking all paths to an Iranian nuclear bomb".

The unilateral withdrawal came despite other parties to the agreement - Britain, China, France, Germany, Russia and the EU - pleading with Mr Trump not to abandon the pact aimed at blocking Iran from acquiring a nuclear weapon, and highlights the US leader's go-it-alone style and his distaste for multilateral agreements.

In an executive order yesterday, Mr Trump said the sanctions seek to pile financial pressure on Iran to force a "comprehensive and lasting solution" to Iranian threats, including its development of missiles and regional "malign" activities.

The impact of the return of sanctions has ramped up tension inside Iran, which has seen days of protests and strikes in multiple towns and cities over water shortages, high prices and wider anger at the political system.

Severe reporting restrictions have made it impossible to verify the swirl of claims coming through social media.

Mr Trump said he was open to reaching a more comprehensive deal with Iran "that addresses the full range of the regime's malign activities, including its ballistic missile programme and its support for terrorism".

But Iranian President Hassan Rouhani was unimpressed by the offer.

"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," the Iranian leader said in an interview on state television.

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

John Glaser, director of foreign policy studies at the Cato Institute, noted that 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".

The second phase of US sanctions, which takes effect on 5 November and will block Iran's oil sales, is due to cause more damage, but several countries including China, India and Turkey have indicated they are not willing to entirely cut their Iranian energy purchases.

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

Russia said it was "deeply disappointed" by the sanctions.

"We are deeply disappointed by US steps to reimpose its national sanctions against Iran," the Russian foreign ministry said in a statement, adding it will do "everything necessary" to save the historic 2015 Iran nuclear deal and protect its shared economic interests with Tehran.