They will directly affect companies from third countries doing business with Iran. They could upset world oil markets, though the US has granted temporary waivers to eight jurisdictions to continue importing Iranian oil.
Iran's supreme leader Ayatollah Ali Khamenei denounced the measures on Saturday, saying Trump had "disgraced" US prestige and would be the ultimate loser in the long-running quarrel between the countries. The US side was unmoved.
World oil markets were on alert, nervously set to gauge the consequences of the sanctions.
The US stance has already inflicted serious pain on Iranians, with the country's currency, the rial, losing more than two thirds of its value since May.
Asked if the US had firm commitments from India and China to stop all oil purchases from Iran within six months, Pompeo replied: "Watch what we do. Watch as we've already taken more crude oil off the market than any time in previous history." Saudi Arabia is the only country with the capacity to make up for lost Iranian oil production.
Hours before the fresh sanctions went ahead, thousands of people in Iran marked the anniversary of the 1979 hostage-taking at the US embassy by carrying placards mocking Trump and burning American flags and fake dollars.
Trump has long argued that the 2015 nuclear deal is badly flawed, in part because its provisions would expire in 10 to 15 years and partly because it does not adequately constrain Iran's destabilising behaviour in the region.
His decision was widely criticised abroad and by Democrats at home, who said that while imperfect, the pact had placed the Iranian nuclear programme under the tightest scrutiny ever.
And Pompeo said that any Iranian banks involved in "sanctionable behaviour will be sanctioned by the Department of Treasury, period, full stop."
The European Union has established a mechanism to permit its multinational companies to maintain presences in Iran, but all signs are that the US sanctions will be dissuasive. Both Airbus and Total have announced plans to leave Iran.
To continue exporting crude oil, Iranian tankers in recent weeks have been turning off their transponders to avoid detection. But satellites have continued to track them.
(This story has not been edited by Business Standard staff and is auto-generated from a syndicated feed.)