The new sanctions will be directed toward energy, shipping, shipbuilding, and financial sectors, representing the "final round of snapback sanctions" as a result of the United States' withdrawal from the Obama-era Iran nuclear deal (formally known as the Joint Comprehensive Plan of Action, or JCPOA), they said.
The measures restore all the United States sanctions that had been lifted under the accord that gave Iran billions of dollars in sanctions relief in exchange for curbs on its nuclear program.
US Secretary of State Mike Pompeo said the waivers, which expire in six months, were necessary to avoid disruption of world oil markets and to give the eight countries more time to eliminate their imports.
Oil prices dipped on Monday as the start to US sanctions against Iran's fuel exports was softened by waivers that will allow some countries to still import Iranian crude, at least temporarily.
The US has re-imposed all of the sanctions against Iran that had been suspended under the 2015 nuclear deal.
"And isn't this a retreat for the United States?" he added.
China, which has been Trump's main sparring partner on the trade front, is Iran's main oil customer.
India hopes to continue to buy about 1.25 million tonnes of oil a month until the end of the fiscal year to March 31, unchanged from November's level, a government official said.
Meanwhile, in Tehran, demonstrators poured onto the streets to mark the 39 anniversary of the occupation of the USA embassy there, an action that precipitated a protracted hostage standoff that helped tank President Carter's chances at re-election and almost took down the Reagan administration amid the Iran-Contra scandal. "If you wanted negotiations, first of all, the easiest way of doing so would be to actually honor the existing deal and ask for additional negotiations on top of the existing deal", he said.
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The Iranian military launched two days of air defense drills on Monday across northern Iran, and state TV aired footage of surface-to-air missiles and air defense systems.
Asked if the U.S. had firm commitments from India and China to stop all oil purchases from Iran within six months, Pompeo replied: "Watch what we do".
European countries which are still party to the 2015 accord have said they will help businesses bypass the sanctions.
German automaker Daimler called off the production and sale of Mercedes-Benz trucks in Iran indefinitely after the sanctions came into force.
But Mr Rouhani struck a defiant tone, saying that Iran would "continue selling oil". If there were any, the U.S. would "aggressively pursue our remedies", he said. The U.N.'s atomic energy agency, which was tasked with monitoring the implementation of the agreement, has certified in multiple reports that Iran is in compliance.
Another signatory to the nuclear deal, China, has said it regrets the the re-imposition of sanctions and that its lawful trade with Iran should be respected.
German and European resistance to U.S. sanctions on Iran appears to be failing, in an apparent victory for Donald Trump's foreign policy.
The sanctions in the aggregate are already having an enormous effect on Iran, he said.