The latest sanctions by the Trump administration was the second batch of its kind after the United States announced its withdrawal from the 2015 Iran nuclear deal in May, signaling the revival of all sanction measures that had previously been lifted under the landmark pact.
"Treasury's imposition of unprecedented financial pressure on Iran should make clear to the Iranian regime that they will face mounting financial isolation and economic stagnation until they fundamentally change their destabilising behaviour", Mr Mnuchin said in a statement.
In addition to hitting Iran's energy sector, Monday's sanctions will target Iran's shipping, shipbuilding and financial sectors. Over the past year, the exchange value of Iran's currency has dropped sharply against the USA dollar.
Two of the countries have agreed to reduce imports to zero while six others "will import at greatly reduced levels", Pompeo said.
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Iranian President Hassan Rohani said in speech broadcast on state TV on Monday that Iran would break the sanctions and continue to sell its oil. "We expect to see more progress as our sanctions start to bite".
They aim to significantly reduce Iran's oil exports - which have already fallen by around one million barrels a day since May - and cut it off from global finance.
Senior Iranian officials have dismissed concerns about the impact to its economy. But the official said that because a stronger oil supply is anticipated for next year, "that will allow us to accelerate the path to zero" imports from Iran. "We have the knowledge and the capability to manage the country's economic affairs", Foreign Ministry spokesman Bahram Qasemi told state TV on Friday.
The same day as the sanctions were reimposed, SWIFT, the Belgium-based bank messaging system, suspended some Iranian banks from using its system.
The president added, "Some think that we negotiated and came to conclusion in nuclear talks which was as a great success, but the USA ruined this success". Iran and five world powers (Russia, the United Kingdom, China, France and Germany) plan to observe the deal.
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The sanctions are created to push Iran's exports to zero.
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".
The U.S. unleashed a fresh wave of sanctions against Iran on Monday, targeting its crude oil exports and its shipping and banking sectors.
Iranian oil accounted for about 5 percent of Japan's crude oil imports before purchases were cut.
News of waivers on the sanctions weighed on prices, analysts said.
Despite such efforts, condensate from Iran is still preferred by local oil-refining and chemical companies due to its lower prices. Many should choose the United States, or have already done so.
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British Prime Minister Theresa May's Downing Street office said Tuesday that the United Kingdom will continue to expand trade relations despite the decision.