Pompeo on Monday also took aim at one of the more insidious elements of Obama's diplomatic strategy, which was that the countries most effected by the change in USA policy toward Iran - Israel and America's Arab allies - were not included in negotiations.
"The sting of sanctions will only grow more painful if the regime does not change course from the unacceptable and unproductive path it has chosen for itself and the people of Iran", Pompeo said in his first major speech since becoming secretary of state.
Pompeo demanded Iran "permanently and verifiably abandon" its nuclear work "in perpetuity", provide worldwide inspectors "unqualified access to all sites throughout the country", halt its ballistic missile program, release detained Americans, and end support for Middle East militant groups.
In his first major foreign policy address since moving to the State Department from the Central Intelligence Agency, the longtime Iran hawk and ardent opponent of the 2015 nuclear pact outlined an aggressive series of moves created to counter Tehran, which he called the world's top sponsor of terror.
So, Iran remains a problem, the United States is more isolated and less trusted overseas, and Iran is now able to, at a time of its choosing, turn up the nuclear pressure, because the nuclear accord is on life support.
Pompeo said a stronger pact should require that Iran stop enrichment of uranium, which was allowed within strict limitations under the previous deal.
The fact is: The Trump team does not have a plan or a strategy for how to get Iran to do any of the things that the United States rightly wants. "At the end of the day, the Iranian people will put a time line" on their government, he said.
Pompeo warned that if Iran fully resumed its nuclear program Washington would be ready to respond and said the administration would hold companies doing prohibited business in Iran to account.
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"We are going to take steps necessary to address Iran's malign influence in the region", Defense Department spokesman Rob Manning told reporters at the Pentagon.
"These will be the strongest sanctions in history by the time we are done", he added.
Some European corporations, like the French automotive manufacturer Peugeot, have, in fact, suggested withdrawing from the deal, citing concerns about obtaining USA sanctions waivers. "Iran will never again have carte blanche to dominate the Middle East". It said Iran could still shoot off those ballistic missiles, obviously meant to transport nukes someday. If Iran complies, Pompeo said the Trump administration would support a treaty agreement (something Obama did not do) that would give Iran access to American markets and full diplomatic recognition.
Russian Federation and China - two other parties to the agreement - have also criticized the USA move and vowed to maintain trade with Iran.
Iran has been moving ahead to build nuclear weapons.
And he also strongly hinted that the Iranian people ought to overthrow their leaders.
European Union foreign policy chief Federica Mogherini also criticised the US.
Pompeo also cautioned European firms against continuing to do business in Tehran, toughening up the United States policy line after its withdrawal from the 2015 nuclear pact this month despite intense diplomatic efforts by Washington's European allies.