US President Donald Trump threatened to obliterate parts of Iran if it attacked "anything American", in a new war of words with Tehran after it condemned the latest US sanctions and called White House actions "mentally retarded".

Key points: Mr Trump made the threat against Iran in a series of tweets

Mr Trump made the threat against Iran in a series of tweets The tweets follow new US sanctions against Iran's Supreme Leader

The tweets follow new US sanctions against Iran's Supreme Leader The Iranian President says new sanctions against Mr Khamenei would have no practical impact

Mr Trump on Monday signed an executive order imposing largely symbolic economic sanctions against Iranian Supreme Leader Ayatollah Ali Khamenei and other senior figures, with punitive measures against Foreign Minister Mohammad Javad Zarif expected later this week.

Iran shot down a US drone last week and Mr Trump said he had called off a retaliatory air strike with minutes to spare, saying too many people would have been killed.

It would have been the first time the US had bombed the Islamic Republic in four decades of mutual hostility.

In rhetoric similar to the kind of harsh words he used to aim at North Korea, Mr Trump tweeted: "Any attack by Iran on anything American will be met with great and overwhelming force. In some areas, overwhelming will mean obliteration."

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In a televised address on Tuesday, Iranian President Hassan Rouhani said the new sanctions against Mr Khamenei would have no practical impact because the top cleric had no assets abroad.

Mr Rouhani, a pragmatist who won two elections on promises to open Iran up to the world, said the White House's actions were "mentally retarded" — an insult that other Iranian officials have used in the past about Mr Trump, but a departure from Mr Rouhani's own comparatively measured tone over the years.

"Tehran's strategic patience does not mean we have fear," said Mr Rouhani, who with his cabinet runs Iran's day-to-day affairs while Mr Khamenei, in power since 1989, is the country's ultimate authority.

US President Donald Trump and Iran's Supreme Leader Ayatollah Ali Khamenei. ( AP/Reuters )

Escalating US sanctions

According to the Iranian Students' News Agency (ISNA), Mr Rouhani told French President Emmanuel Macron in a phone call on Tuesday that Iran was not looking for war with America.

But Mr Rouhani told Mr Macron that if the US violated Iran's territorial space again, as Iranian officials maintain a US drone did last week, it would be confronted.

"If the Americans want to violate the waters or airspace of Iran again, Iran's armed forces have a duty to confront them and they will have a decisive clash," Mr Rouhani said.

Mr Rouhani also told Mr Macron that Iran would not renegotiate the 2015 nuclear deal, ISNA reported.

The US has imposed crippling financial sanctions against Iran since last year, when Mr Trump withdrew from a 2015 deal between Tehran and world powers under which Iran curbed its nuclear program.

Tension has escalated sharply since last month when the Trump administration tightened its sanctions noose, ordering all countries to halt purchases of Iranian oil.

That has effectively starved the Iranian economy of the main source of revenue Tehran uses to import food for its 81 million people, and left the pragmatic wing of Iran's leadership, led by Mr Rouhani, with no benefits to show for its nuclear agreement.

Space to play or pause, M to mute, left and right arrows to seek, up and down arrows for volume. Watch Duration: 53 seconds 53 s Trump signs executive order targeting Iranian leadership

Mr Trump said the accord reached under his predecessor, Barack Obama, was a failure because its terms were not permanent and did not cover security issues beyond Iran's nuclear program, such as its missiles and role in various Middle East conflicts.

The downing of the US drone — which Iran said was over its air space but the US maintained was in international skies — followed weeks of rising tensions that had begun to take on a military dimension.

Mr Trump's hawkish national security adviser, John Bolton, while visiting Israel repeated earlier offers to hold talks, as long as Iran was willing to go beyond the terms of the 2015 deal.

"The President has held the door open to real negotiations to completely and verifiably eliminate Iran's nuclear weapons program, its pursuit of ballistic missile delivery systems, its support for international terrorism and other malign behaviour worldwide," Mr Bolton said in Jerusalem.

"All that Iran needs to do is to walk through that open door."

Iran says there is no point negotiating with Washington when it has abandoned a deal already reached.

Foreign Ministry spokesman Abbas Mousavi said imposing "useless sanctions" on Mr Khamenei and Mr Zarif would mark "the permanent closure of the path of diplomacy."

Russian Foreign Minister Sergei Lavrov warned that the situation surrounding Iran was developing toward a dangerous scenario, the RIA news agency reported on Tuesday.

The US and some regional allies have blamed Iran for explosions that damaged tankers in the Gulf, but Tehran denies it was responsible.

Washington's European allies have repeatedly warned both sides of the danger that a small mistake could lead to war.

Tehran has given European signatories until July 8 to find a way to shield its economy from US sanctions, or else it will enrich uranium to higher levels banned under a deal designed to prevent the development of a nuclear weapon.

Acting US Defence Secretary Mark Esper said he hoped to recruit support from NATO allies in Brussels this week for US efforts to deter conflict with Iran and "open the door to diplomacy", as he made his first trip as Pentagon chief.

Space to play or pause, M to mute, left and right arrows to seek, up and down arrows for volume. Watch Duration: 17 seconds 17 s The attacks left one tanker on fire and all sailors were evacuated from both ships

Reuters