The move restored US sanctions that were lifted under a 2015 nuclear deal negotiated by the administration of President Barack Obama, and added 300 new designations in Iran's oil, shipping, insurance and banking sectors.
In May, President Donald Trump pulled the USA out of + the 2015 landmark Joint Comprehensive Plan of Action (JCPOA) terming it as "disastrous".
The Europeans are working to set up a special payment system that would bypass the United States sanctions and discard the dollar in dealings with Iran.
But Mr Rouhani struck a defiant tone, saying that Iran would "continue selling oil". Washington says it wants a new deal with Iran, curtailing its regional interventions and missile programme - demands which have been flatly rejected by Tehran.
Mr Rouhani said four countries had approached him during his visit to NY for the UN General Assembly in September, offering to mediate with the USA, but he turned them down.
'We are in the economic war situation.
The Trump administration's decision to restore sanctions "is the sea change the Middle East has been waiting for", he said.
Switzerland said it was holding talks with the United States and Iran about launching a humanitarian payment channel to help food and drugs keep flowing to Tehran. Iranian army Gen. Habibillah Sayyari said both the national army and the country's paramilitary Revolutionary Guard were taking part in the exercise.
Before travelling to a campaign rally for the USA midterm elections, President Trump said Iran was already struggling under his administration's policies.
South Korea was also granted an exemption from Washington to continue financial transactions with the sanctioned Iranian central bank to facilitate oil imports, according to the official.
Rouhani, meanwhile, pledged to government officials in comments aired on state TV that Iran would overcome the sanctions. "That's who really understand the importance and the impact of the effort that we're undertaking". Experts predict oil exports will drop further in the near future.
On Friday Secretary Mnuchin and Pompeo held a conference call with reporters explaining the scope of sanctions.
China said on Monday its lawful trade cooperation with Iran should be respected and expressed regret that the United States re-imposed sanctions on the Middle Eastern country.
Part of the explanation lies in the ambiguous position of the USA, which initially insisted that the sanctions were created to reduce Iranian exports to zero barrels, but has since has softened its position. The move incensed US allies in western Europe, who had begun to make significant investments in Iran, as a result of the Obama-era nuclear pact, known as the Joint Comprehensive Plan of Action, or JCPoA.
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