Mr Rouhani said his country would continue to sell oil and would break Washington’s punitive embargoes on its vital energy and banking sectors.
He said: “America wanted to cut to zero Iran’s oil sales but we will continue to sell our oil to break sanctions.”
The measures came into force today after US President Donald Trump pulled out of the Iran nuclear deal earlier this year and reimposed a first round of sanctions on the Islamic republic in August.
Mr Rouhani said on state TV on Monday his nation was is in a “situation of economic war” and was ”confronting a bullying power”.
He said his country will “proudly bypass” Donald Trump’s “illegal” and “unjust” sanctions by selling oil.
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He said: “I announce that we will proudly bypass your illegal, unjust sanctions because it’s against international regulations.
“We are in a situation of economic war, confronting a bullying power.
“I don’t think that in the history of America, someone has entered the White House who is so against law and international conventions.”
Mr Trump’s secretary of state Mike Pompeo has defended the sanctions and heralded them as the “toughest” ever put in place on the country.
Thousands of Iranian students chanted “death to America” on the eve of the sanctions, which target the Middle Eastern country’s vital energy and banking sectors.
US flags, an effigy on Uncle Sam and pictures of Mr Trump were set on fire in images broadcast on state TV.
The Iran nuclear deal was drawn up by the Obama administration and was agreed to by the UK, Russia, France, China, Germany and the EU.