Iranian President quickly dismissed the threats, saying the rest of the world no longer accepts Washington making decisions on their behalf.
Washington: US Secretary of State Mike Pompeo on Monday warned Tehran would be hit with the "strongest sanctions in history" and cautioned European firms against continuing to do business with it, toughening up Washington's policy line after its withdrawal from the Iran nuclear deal.
In his first major foreign policy address since moving to the State Department from the CIA, the longtime Iran hawk and ardent opponent of the 2015 nuclear pact outlined an aggressive series of moves designed to counter Tehran, which he called the world's top sponsor of terror.
"We will apply unprecedented financial pressure on the Iranian regime. The leaders in Tehran will have no doubt about our seriousness," Pompeo said in a speech at the conservative Heritage Foundation think tank.
"This sting of sanctions will be painful if the regime does not change its course from the unacceptable and unproductive path it has chosen to one that rejoins the league of nations."
Iranian President Hassan Rouhani quickly dismissed the threats, saying the rest of the world no longer accepts Washington making decisions on their behalf.
"Who are you to decide for Iran and the world?" Rouhani said in a statement carried by multiple Iranian news agencies.
"The world today does not accept that the United States decides for the world. Countries have their independence," he added.
Pompeo said if Iran were to abide by stricter terms, including ending its ballistic missile program and its interventions in regional conflicts from Yemen to Syria, the United States would lift its new sanctions.
President Donald Trump has long said the 2015 deal with Iran -- also signed by Britain, China, France, Germany and Russia -- did not go far enough, and now wants the Europeans and others to support his hardline strategy.
The deal was designed to prevent Iran from developing a nuclear weapon. The international community, including top US officials, have said Tehran had been in compliance.
But Trump despised the deal, pointing to other aspects of Iranian behaviour not covered in the pact, and on May 8 he pulled America out despite intense diplomatic lobbying by European allies who had beseeched him to stick with it by adding tougher new elements.
Instead of suggesting a re-negotiation of the Iran deal, Pompeo outlined 12 tough conditions from Washington for any "new deal" with Tehran to make sure it "will never again have carte blanche to dominate the Middle East."
These essentially address every aspect of Iran's missile program and what the US calls its "malign influence" across the region, including support for Syrian President Bashar al-Assad, Hezbollah and Huthi rebels in Yemen.
"It must cease its threatening behaviour against its neighbours," Pompeo said.
Rouhani compared the comments as akin to those made by the administration of George W. Bush ahead of the 2003 Iraq invasion.
"The era of such statements has evolved and the Iranian people have heard these statements hundreds of times, and no longer pays attention," Rouhani added.
Iran foe Israel's Prime Minister Benjamin Netanyahu hailed Pompeo's speech, and urged the rest of the world to follow suit.
"The US policy is correct. Iran is spreading aggressively throughout the Middle East. It aspires to achieve nuclear weapons by various means," Netanyahu said.
European allies heard how Pompeo expects their support for the new US plan -- but he offered nothing in return, and threatened economic fallout for anyone still dealing with the Islamic Republic.
"We understand that our re-imposition of sanctions and the coming pressure campaign on the Iranian regime will pose financial and economic difficulties for a number of our friends," he said.
"We want to hear their concerns. But you know, we will hold those doing prohibited business in Iran to account."
The re-establishment of US sanctions will force European companies to choose between investing in Iran or trading with the United States.
In reality, there is no choice -- European companies cannot afford to forsake the US market.
For now, the European Union is trying to persuade Iran to stay in the 2015 agreement, even without Washington's participation.
Russia and China have also criticized the US move and vowed to maintain trade with Iran.
British Foreign Secretary Boris Johnson said the sort of "jumbo Iran deal" Pompeo envisioned would not be "very easy to achieve in anything like a reasonable timescale."
And the EU's foreign policy chief said there was "no alternative" to the Iran nuclear deal.
"Secretary Pompeo's speech has not demonstrated how walking away from the JCPOA (nuclear deal) has made or will make the region safer from the threat of nuclear proliferation or how it puts us in a better position to influence Iran's conduct in areas outside the scope of JCPOA," Federica Mogherini said.
Critics rounded on Pompeo's speech, saying his demands could have been made without pulling America from the nuclear deal.
"Pompeo has not outlined a strategy, but rather a grab bag of wishful thinking that can only be interpreted as a call for regime change in Iran," Suzanne Maloney of the Brookings' Centre for Middle East Policy wrote on Twitter.
Meanwhile, Pentagon spokesman Colonel Rob Manning said the military was weighing "new actions" to counter Iran's influence in the Middle East, but he stressed this was part of a "whole of government" approach and offered no details.