The most significant of the new measures is a prohibition against oil and gas sales, which provide the Iranian Government with 80 per cent of its total revenue.
"We are in a situation of economic war, confronting a bullying power".
The ministry's spokesman, Baharam Ghasemi said the sanctions would backfire and work against the U.S. and that "many countries from Europe to Russian Federation and China have opposed the sanctions".
The US President said documents "conclusively" showing the Iranian regime was pursuing nuclear weapons informed his decision to pull out of the landmark nuclear agreement.
Iranian state media claimed millions of people had turned out for rallies in most cities and towns around the country - a figure that has not yet been independently verified.
"Since the Trump administration came into office we've done 19 round of sanctions, targeting 168 Iranian entities", stated Pompeo.
"I announce that we will proudly bypass your illegal, unjust sanctions because it's against global regulations", he said.
"It's black humour but the audience can also be brought to reflect on the contradictions in the behaviour of Trump and Al Saud", he said, standing in front of a cartoon showing an old wheelchair-bound figure dressed like a comic-book superhero.
Pompeo, in an interview broadcast on Fox News Sunday, predicted the sanctions would be successful.
Asked if the USA had firm commitments from India and China to stop all oil purchases from Iran within six months, Pompeo replied: "Watch what we do".
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"We continue negotiations to get all of the nations to zero", he said.
Trump warned that those who don't wind down their economic ties to Iran "risk severe consequences".
Eight countries, including Turkey, India and Japan, have been given temporary exemptions by the U.S., so they can keep purchasing oil and see stability in their economies and the global oil supply.
Oil is Iran's main source of income.
His decision was widely criticized overseas and by Democrats at home, who said that while imperfect, the pact had placed the Iranian nuclear program under the tightest scrutiny ever. Its national currency, the rial, now trades at 145,000 to one U.S. dollar (£0.77), down from when it traded 40,500 to $1 a year ago.
But the sanctions will not affect Iran's trade with the rest of the world.
Washington has so far not identified the eight. "And we'll see what happens with Iran, but they're not doing very well, I can tell you".
Mr Rouhani said four countries had approached him during his visit to NY for the UN General Assembly in September, offering to mediate with the USA, but he turned them down. Cruz said it was important that "final policy imposes maximum pressure" on Tehran.
However, Trump's national security advisor, John Bolton, and personal lawyer, Rudy Giuliani, have publicly supported toppling the Iranian government and leadership.
He said the list would be provided on Monday, when the new sanctions are set to take effect.
ASSOCIATED PRESS A rally against "Uncle Sam" was held in central Tehran on Sunday ahead of re-introduced U.S. sanctions.
Secondary sanctions also mean that any United States company doing business with a company that trades with Iran could face punishment. It was also allowed to continue financial transactions with the Middle East country, it said. Known as the Joint Comprehensive Plan of Action (JCPOA), the deal with Iran was signed by the United States, Germany, the United Kingdom, China, Russia, France and the European Union.