The move restored USA sanctions that were lifted under a 2015 nuclear deal negotiated by the administration of President Barack Obama, and added 300 new designations in Iran's oil, shipping, insurance and banking sectors.
Meanwhile, Iranian president, Hassan Rouhani, has responded robustly, saying: "There is no doubt that the United States will not achieve success with this new plot against Iran as they are retreating step by step".
The restoration of USA sanctions on Monday targeting Iran's oil sales and banking sectors is part of a wider effort by Trump to force Tehran to halt its nuclear and ballistic missile programmes outright, as well as support for proxy forces in conflicts across the Middle East.
Iran reached an agreement with the six world powers including the US and the European Union in 2015, which curtailed its nuclear programme in return for lifting of the global economic sanctions.
On Sunday, hard-liners vented their rage at a new American president, Donald Trump, who pulled the United States out of the nuclear deal struck by his predecessor that the United Nations said Tehran still honours.
The new wave of sanctions, the second since August, will target Iran's energy, shipbuilding, shipping, and financial sectors. Contrary to what he called "fueled misinformation", he stated that SWIFT, "if it provides financial messaging services to certain designated Iranian financial institutions...could be subject to sanctions".
"Never threaten Iran, ' he warned US President Donald Trump, describing him as America's 'strange president". He qualified that transactions for "humanitarian" purposes would be exempt, as they had been in the past, but cautioned that "banks must be very careful that these are not disguised transactions".
"We are in the war situation", Rouhani said.
Rouhani, meanwhile, pledged to government officials in comments aired on state TV that Iran would overcome the sanctions.
Successive US presidents have used the reserve currency status of the US dollar as a weapon to isolate the country's enemies and to enforce its will.
If the U.S. had not granted waivers to China and some of the other countries, they would have also ignored the sanctions.
Asked if the USA had assurances from India and China - suspected to be among the nations getting waivers - that they would eventually give up importing oil from Iran, Pompeo wouldn't say.
Since Mr Trump said in May that he would reimpose sanctions, two big developments may have affected his thinking.
South Korea, one of Asia's biggest buyers of Iranian oil, last week asked the United States for "maximum flexibility" after some of its construction firms cancelled energy-related contracts in the Islamic Republic because of financing difficulties.
Iran is already in the grip of an economic crisis. The rial now trades at 145,000 to $1, compared with 40,500 to $1 a year ago.
Threatening more directly, Salami claimed that "battle with the Islamic Republic will take the war beyond the region" and "if we want, in a short time we can establish dominance over the U.S.in the Middle East".
The symbolism of the looming sanctions coming wasn't lost on protesters Sunday.
The U.S. will issue waivers on Iranian oil to eight jurisdictions.