Individuals or entities that fail to wind down activities with Iran risk severe consequences.
The renewed sanctions were among those lifted under a 2015 deal between world powers and Tehran on curbing Iran's nuclear program.
The Iranian regime is facing a mounting challenge from within.
Trump pulled the United States out of the deal in May, saying Iran was not living up to the spirit of the accord and vowed to reimpose sanctions.
Outside U.S. borders, however, the Trump administration's decision to snap sanctions back into place has been received with a mixture of regret, anger and alarm - especially among the other countries that engaged in the deal, and that have promised to stick with it despite the U.S. decision to renege on its commitment.
The European Union on Monday said that new measures are ready to take effect to protect European businesses from the impact of US sanctions on Iran. "Yet the very first sanctions it reimposed have canceled licenses for sales of 200+ passenger jets under absurd pretexts, endangering ordinary Iranians", the country's foreign minister, Javad Zarif, tweeted Monday.
The comment came just hours after Jeremy Hunt, the Foreign Secretary, issued a joint statement with the foreign ministers of Germany, France and the European Union expressing "deep regret" at America's decision to reimpose sanctions. But he said Iran must change its ways.
Speaking to IRIB, Rouhani said Trump's offer to negotiate is aimed at "creating divisions" in Iran, accusing him of trying to launch a "psychological warfare" against the Iranian people.
Basically, Trump withdrawing from the deal dealt Iran a huge blow, which will significantly hurt its earning potential and liquidity.
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Right before the briefing began, the White House released a letter Bolton sent to Senate Democrats about election interference. Bolton said Trump is "leading unprecedented action to punish Russia" for its efforts to disrupt American elections.
But questions persist as the administration appears to welcome the collapse of Iran's economy and voice louder and louder support for protests against the regime for the economic state.
Secretary of State Mike Pompeo said Monday that the sanctions will "counter its malign activities".
A senior administration official said Brussels" imposition of a "blocking statute" protecting European businesses trading with Iran was "not something we're particularly concerned by'. The fall of prices for the rial has been heavy related to the surge in the price of gold, as economic uncertainty has many Iranians running to precious metals, and gold imports surged in recent weeks.
"This is an important moment for Israel, for the United States, for the region, and for the entire world", Prime Minister Benjamin Netanyahu said in a video released moments after Trump signed new sanctions into law.
Trump's controversial decision to rescind U.S. participation in the JCPOA paved the way for the reimposition of sanctions in two stages: the first batch will kick in on Tuesday, 90 days after the country's withdrawal; the second round will take effect on 4 November, at the 180-day mark after the USA departure.
The arrival of the ATR72-600 airplanes at Tehran's Mehrabad International Airport represented perhaps the last benefits Iran will see under the nuclear deal after President Donald Trump withdrew from it in May.
Those sanctions had been lifted by the Obama administration under the terms of the landmark deal in 2015 that gave Tehran an infusion of cash, which the USA says paid for terrorist activities.