The snapback sanctions are meant to target Iran's purchases of United States dollars, metals trading and other dealings, coal, industrial-related software and its auto sector.
The second phase of U.S. sanctions, which takes effect on 5 November and will block Iran's oil sales, is due to cause more damage, but several countries including China, India and Turkey have indicated they are not willing to entirely cut their Iranian energy purchases.
European companies will be protected from the impact of new sanctions imposed by the U.S. on Iran, Britain has said.
Iran is accusing the USA of reneging on the nuclear agreement, signed by the Obama administration, and of causing recent Iranian economic unrest. European allies said they "deeply regret" the United States action.
He blasted the agreement yet again yesterday, calling it a "horrible, one-sided deal (that) failed to achieve the fundamental objective of blocking all paths to an Iranian nuclear bomb".
The two other signatories to the 2015 pact - Russian Federation and China - also continue to support it.
Asked about threats to close the Strait of Hormuz, Mr Bolton said that would be Iran's "worst mistake yet".
"Prices are rising again, but the reason is government corruption, not U.S. sanctions", said Ali, a 35-year-old decorator in Tehran. But on Iran, Mr Trump now has a team who share his contempt for the regime and are even more determined to see its end.
With US sanctions set to return against Iran on Tuesday, Zarif acknowledged there were hard times ahead. He said Tehran has always believed in resolving disputes diplomatically.
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"Anyone doing business with Iran will NOT be doing business with the United States", the president tweeted.
"If you stab someone with a knife and then you say you want talks, then the first thing you have to do is remove the knife", Rouhani said in a speech broadcast live on state television. "But talks need honesty".
Iran's central bank, acting on the eve of the USA move, scrapped most currency controls introduced this year in a bid to halt a plunge in the rial that has stirred protests against the government.
Iranians are already seeing the effects of the sanctions, with Iran's rial currency losing around half its value since Mr Trump announced the USA would withdraw from the 2015 nuclear accord.
He added, "To this day, Iran threatens the United States and our allies, undermines the global financial system, and supports terrorism and militant proxies around the world". "But if the government has a serious plan they can control the situation".
The European Union has also spoken out against the sanctions, vowing to protect firms doing "legitimate business".
The European commission today put in place never-before-used legislation to protects the continent's firms from USA sanctions which not only target Tehran but their trading partners.
"The remaining parties to the JCPOA have committed to work on, inter alia, the preservation and maintenance of effective financial channels with Iran, and the continuation of Iran's export of oil and gas", the joint statement between the European Union and the E3 highlighted.