"The U.S. remains open to reaching a new, more comprehensive deal with Iran that forever blocks its path to a nuclear weapon, addresses the entire range of its malign actions, and is worthy of the Iranian people", Mr. Trump said in a presidential statement late on Friday night.
In addition to the countries allowed to continue buying Iranian oil, the backing of China, Iran's largest trading partner, may also prove critical.
The late founder of the Islamic Republic, Imam Khomeini, hailed the takeover as a "second revolution" after the 1979 Islamic Revolution toppled the Shah of Iran, who was a close ally of the U.S. in Iran.
Diplomats told Reuters last week that the new European Union mechanism to facilitate payments for Iranian exports should be legally in place by November 4, when the next phase of United States sanctions hit, but will not be operational until early next year. "The other six will import at greatly reduced levels", Pompeo said.
Friday's announcement came just days before congressional midterm elections in the US, allowing Mr. Trump to highlight his decision to withdraw from the deal - a move that was popular among Republicans.
Later, a senior State Department official told reporters that that the US was ready for talks with Iran. "We have the knowledge and the capability to manage the country's economic affairs", Iran's Foreign Ministry spokesman, Bahram Qasemi, told state television. "We have advised SWIFT that it must disconnect any Iranian financial institutions that we designate as soon as technologically feasible to avoid sanctions exposure".
Pompeo defended the oil waivers and noted that since May, when the USA began to press countries to stop buying Iranian oil, Iran's exports had dropped by more than 1 million barrels per day.
"There's a key fact here: in this 40-year challenge, the defeated is the United States and the victorious is the Islamic republic".
The impact of the sanctions has already been cushioned by other oil producers, notably some of Iran's counterparts in the Organisation of Petroleum Exporting Countries.
"And just today, we riposted all sanctions that were lifted under that awful deal".
Countries with close security and trade ties with the United States were quick to cut their purchases - South Korea went nearly straight to zero, with Japan and much of Europe close behind.
The US has made it clear it wants eventually to cut off Iran's oil trade entirely, but has allowed eight countries to maintain imports as a temporary concession to give them time to reduce imports.
As a result of the latest sanctions, he said the USA expects to have reduced Iranian crude oil exports by more than 1 million barrels even before these sanctions go into effect.
The report discusses an unsealed indictment in the USA which "provides detail on Iran's use of deceptive practices to procure export controlled items with military applications from the U.S. and elsewhere".