The sanctions end all the economic benefits America granted Tehran for its 2015 nuclear deal with world powers, though Iran for now continues to abide by the accord that saw it limit its enrichment of uranium.
Swift now needs to decide whether or not to abide by the USA demand - a decision that could involve breaking European Union rules - although it may well be that banks will now shun Iranian transactions whatever Swift decides.
US Secretary of State Mike Pompeo said on Sunday the penalties returning on Monday were "the toughest sanctions ever put in place on the Islamic Republic of Iran".
Iran's Supreme Leader, ayatollah Ali Khamenei also attacked the United States and President Donald Trump a day earlier, on November 3, criticizing those who advocate negotiations with Washington.
"America wanted to cut to zero Iran's oil sales.but we will continue to sell our oil.to break sanctions", Rouhani told economists, adding the sanctions were illegal and unfair.
'We are in the economic war situation. America should learn that it can not use the language of force against Iran ...
"We are in the war situation", he said.
He said Washington's violation of worldwide law has made the USA more isolated than ever. We are confronting a bullying enemy. President Trump withdrew from the deal in May, and has since reimposed sanctions in 19 rounds. The other parties to the deal - Britain, France, Germany, China and Russian Federation - say they will not leave.
Under US law, exceptions can be granted for up to 180 days. Similarly, Secretary Mnuchin said a list of banks subject to the new sanctions would also be provided on Monday.
Asked on CBS whether Iran could restart its nuclear program, Pompeo said, "We're confident that the Iranians will not make that decision".
Bears remains in control, as Tehran defies USA sanctions and continues oil exports.
In the capital city of Tehran, the rally was held at the venue of the former U.S. embassy, which is known by Iranians as the "Den of Espionage". As long as Iran met its obligations under the deal, Britain would be committed to it too.
"The fact that the USA has exempted eight countries from the sanctions after they threatened to bring Iran oil exports to zero, isn't this a victory for us?"
Asked about the eight exempted countries, White House press secretary Sarah Huckabee Sanders said the USA was exerting intense pressure on Iran.
WTI (oil futures on NYMEX) extended its losing streak into a sixth day today and hit fresh seven-month lows near $ 62.50, now consolidating near the last amid moderate risk-aversion. We've got Brent crude at about the same price it was back in May when the president announced the withdrawal from the JCPOA.
U.S. West Texas Intermediate (WTI) crude futures CLc1 were down 35 cents, or 0.6 percent, at $62.79 a barrel.
They aim to significantly reduce Iran's oil exports - which have already fallen by around one million barrels a day since May - and cut it off from worldwide finance. In granting waivers, Washington is trying to ensure that global oil prices don't spike, especially in the middle of the US election season. Campaigning in Chattanooga, Tennessee, on Sunday, Trump said his "maximum pressure" against Iran was working.
"The whole world understands that these sanctions are real", Pompeo said.
Since May, Europeans have said repeatedly that they want to preserve the nuclear deal and have focused their diplomatic efforts on keeping trade alive with Iran however possible.