"Who are you to decide for Iran and the world?" the Iranian president was quoted as saying. "Countries have their independence", he added.
Brookings Institution Senior Fellow Darrell West told Xinhua that the most important element of Pompeo's speech was the threat to impose the strongest sanctions on Iran in that country's history.
The remarks by Pompeo came almost two weeks after his boss Donald Trump withdrew the US from the 2015 worldwide nuclear deal.
It should be clear by now that Iranian regime's pursuit of nuclear weapons will only be definitively resolved once that regime is no longer in power. "We call on the entire global community to join this American position", Netanyahu added. Trump's move came despite the fact that the UN's nuclear watchdog, in charge of monitoring Iran's compliance with the deal, has confirmed that Tehran has abided by the terms of the agreement.
He said Iran must allow nuclear inspectors "unqualified access to all sites throughout the country", Pompeo said, alluding to military sites that were off-limits under the 2015 deal except under specific circumstances.More news: Israel is world's first country to attack with F35s
These essentially address every aspect of Iran's missile program and what the USA calls its "malign influence" across the region, including support for Syrian President Bashar al-Assad, Hezbollah and Huthi rebels in Yemen.
Rouhani compared the comments as akin to those made by the administration of George W. Bush ahead of the 2003 Iraq invasion. A member of the Iranian parliament's national security committee suggested that the best approach would be to wait for United States policy to change once Trump leaves office.
At the same time, Pompeo offered Iran a series of dramatic potential US concessions if it agrees to make "major changes". "It aspires to achieve nuclear weapons by various means", Netanyahu said. But European companies say they are anxious about getting caught up in the new USA sanctions, given the extent of Washington's global reach, and some have already started pulling out. In a speech on Monday in Washington, America's top diplomat said Iran would be "battling to keep its economy alive" after the sanctions took effect.
Regardless of the future of the JCPOA, the Iranian regime's threat requires a more comprehensive approach. "But you know, we will hold those doing prohibited business in Iran to account".
The re-establishment of the USA punitive measures will likely force European companies to choose between investing in Iran or trading with the United States.More news: GE Transportation reaches agreement to merge with Wabtec
In reality, there is no choice - European companies can not afford to forsake the United States market.
Pompeo vowed to crank up the pressure on Iran with "the strongest sanctions in history", saying the U.S. wanted "the support of our most important allies and partners in the region and around the globe" to implement it.
"Iran will never again have carte blanche to dominate the Middle East", Mr Pompeo said. Federica Mogherini, the high representative of the European Union, explained that Europeans will remain committed to "full and effective implementation" of the JCPOA so long as Iran upholds its commitments.
Measures outlined by Secretary of State Mike Pompeo, he said, showed the U.S. was a prisoner of its "failed policies" and it would suffer the consequences.
Pompeo called Iran out for a wide range of "malign activities" apart from its nuclear program.More news: Pope Francis tells gay man "God made you like this"
In response to a question whether Iran was satisfied with the proposals made by EU Climate Action and Energy Commissioner Miguel Arias Cañete during his recent visit to Tehran, Araqchi said he was unaware of all aspects of the issue.