Video report by ITV News Senior International Correspondent John Irvine
The new US sanctions targeting Iran’s supreme leader and other top officials mean the “permanent closure” of diplomacy as President Hassan Rouhani derided the White House as being "afflicted by mental retardation".
US President Donald Trump called that a "very ignorant and insulting statement", tweeting that an Iranian attack on any US interest will be met with "great and overwhelming force ... overwhelming will mean obliteration".
Speaking in Israel, US national security adviser John Bolton, known to be a longtime advocate for military action against Iran, said the Iranians could walk through an "open door" to talks with America.
But he warned that "all options remain on the table" if Tehran carries through its vow to break its 2015 nuclear deal with world powers - a deal the US pulled out of in 2018.
Iranian Foreign Ministry spokesman Abbas Mousavi said the “useless sanctioning of Islamic Revolution Supreme Leader (Ali Khamenei) and the commander of Iranian diplomacy means closing the doors of diplomacy by the U.S.' desperate administration”.
Donald Trump enacted new sanctions on Monday targeting Iran’s Supreme Leader Ayatollah Ali Khamenei.
US officials also say they are planning sanctions against Iranian Foreign Minister Mohammad Javad Zarif, something that drew Mr Rouhani's anger during his televised address Tuesday.
"You sanction the foreign minister simultaneously with a request for talks," he said.
He called the sanctions against Mr Khamenei "outrageous and idiotic", especially since the 80-year-old supreme leader has no plans to travel to the US.
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"The White House is afflicted by mental retardation and does not know what to do," he added.
US secretary of state Mike Pompeo said he had not heard Mr Rouhani's reaction to the new sanctions, but added that if the reports were true "that's a bit immature and childlike".
"But know that the United States will remain steadfast in undertaking the actions that the president laid out in this strategy to create stability throughout the Middle East, which includes the campaign we have, the economic campaign, the pressure campaign that we have on the Islamic Republic of Iran," he added.
The crisis gripping the Middle East stems from Mr Trump's withdrawal of the US a year ago from the nuclear deal with Iran and other world powers and then imposing crippling new sanctions on Tehran.
Recently, Iran quadrupled its production of low-enriched uranium to be on pace to break one of the deal's terms by Thursday, while also threatening to raise enrichment closer to weapons-grade levels on July 7 if European countries still abiding by the accord do not offer a new deal.
Citing unspecified Iranian threats, the US has sent an aircraft carrier to the Middle East and deployed additional troops alongside the tens of thousands already there.
All this has raised fears that a miscalculation or further rise in tensions could push the US and Iran into an open conflict, 40 years after the Islamic Revolution.
Tuesday's developments come amid heightened tensions between Iran and the US over its unravelling nuclear deal and after Iran shot down a US military surveillance drone last week.
Mr Trump said the supreme leader is responsible for Iran’s hostile conduct.
He said the United States does not seek conflict with Iran but will continue to increase pressure on its Middle East adversary to prevent it from developing nuclear weapons and supporting militant groups.
After signing the sanctions Mr Trump said "the assets of Ayatollah Ali Khamenei and his office will not be spared from the sanctions".
He added: "These measures represent a strong and proportionate response to Iran's increasingly provocative actions.
"We will continue to increase pressure on Tehran until the regime abandons its dangerous activities and aspirations including the pursuit of nuclear weapons."
These exchanges comes as Mr Pompeo visits Saudi Arabia in a hastily arranged visit amid mounting tensions between Washington and Tehran.
Mr Pompeo wrote on Twitter Monday that he had met with Saudi King Salman in the city of Jiddah to discuss the heightened tensions and protecting maritime security in the Persian Gulf.
Mr Pompeo, considered a hard-liner in Washington, referred to Iran as “the world’s largest state sponsor of terror” before he embarked the Middle East trip.
He is also expected to meet Abu Dhabi's powerful Crown Prince Mohamed bin Zayed, before heading to India Tuesday.
Tensions have been rising since the $100m unmanned drone was downed near the Strait of Hormuz.
Mr Trump revealed the US military had been "cocked and loaded" and just 10 minutes away from launching a strike on radar installations and missile batteries in Iran before he called off the action.
Britain's Foreign Secretary Jeremy Hunt has also said he would consider joining any military assault on Iran in support of the US.