"These will be the strongest sanctions in history by the time we are done", he added.
In his fist major foreign policy address since becoming chief diplomat, Pompeo laid out 12 pillars the USA would demand from Iran for a new deal, even as he said a new agreement is "not the objective" of the Trump administration.
Iranian diplomats negotiating to keep the deal alive in Europe are not discussing any other issues, he said.
He also demanded that Iran must withdraw all forces under Iranian command from Syria, end support for the Taliban and other terrorists in Afghanistan and the region, and cease harbouring al-Qaeda, and it must end its Quds Force's support for terrorists and militant partners.
"Iran will not violate the nuclear deal, but if the United States withdraws from the deal, they will surely regret it".
Lorne Baring, chief investment officer at fund management firm B Capital SA said: "There might be some element of arbitration for the European companies in Iran, but ultimately nobody will want to get on the wrong side of United States sanctions".
The United States will "apply unprecedented financial pressure on the Iranian regime" to achieve the new goals, Pompeo said.
The USA has set in motion a series of sanctions that will give Iran 2 choices, surrender or fight.
Formally known as the Joint Comprehensive Plan of Action (JCPOA), the so-called Iran nuclear deal - an Obama-era agreement between Iran and the United States, the United Kingdom, Germany, France, Russia, China, and the European Union - was established to reward Iran for curbing its nuclear program.
Weeks after the United States pulled out of an global nuclear deal with Iran, Pompeo spelled out a hardline approach towards the Islamic Republic that included working closely with the Pentagon and regional allies to contain Iran. Iran must also allow nuclear "unqualified access to all sites throughout the country".
Despite the claims, the International Atomic Energy Agency has repeatedly said that the agreement has successfully halted the weaponisation of Iran's nuclear programme.
"In many ways, it looks as if the U.S. is dictating what should be done when, of course, from the Europeans' point of view there is a deal already there that most European leaders say has been working and they say that Iran has been complying". A longtime Iran hawk, Pompeo has spoken positively about regime change in the past, but in his confirmation hearing last month he sought to soften that stance.
Laying out Trump's new approach Monday, Pompeo said he couldn't put a timeline on how long the strategy might take.
"We acknowledge Iran's right to defend its people".
"This contradiction in the European officials' remarks is dubious", he said, adding, "We hope that our administration officials would be able to receive the necessary guarantees in their negotiations because otherwise, a party that is equivocal and makes contradictory remarks can not be trusted". None of this is news, and his speech left huge questions about the Trump administration's "new Iran strategy" unanswered.
Following US president Donald Trump's withdrawal from the 2015 deal, America will ensure "Iran has no possible path to a nuclear weapon, ever", Mr Pompeo said.
On a more welcomed note, Pompeo said the Trump administration would go the treaty route.
"I think this is for many people here in the Middle East a breath of fresh air when the Trump administration is really holding Iran accountable for all the things they are doing here in the Middle East", Mitchell said shortly after Pompeo's speech.
Pompeo said the USA would respond If Iran restarts nuclear activities, but added, "I'm not prepared to share with you what that response will be". That is their decision to make.