"I announce that we will proudly bypass your illegal, unjust sanctions because it's against international regulations," Rouhani said in a televised speech.
"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," he added.
"Watch what we do. Watch as we've already taken more crude oil off the market than any time in previous history," he told CBS's "Face the Nation" on Sunday.
"Constantly they are sending us messages saying 'Let's sit and negotiate.' Negotiations for what?" said Rouhani.
"First, you respect the negotiations we already concluded, so that there are grounds for the next negotiations."
Rouhani said four countries had approached him during his visit to New York for the UN General Assembly in September, offering to mediate with the US but he turned them down.
"There is no need for mediation. There is no need for all these messages. Act on your commitments, and we will sit and talk," he said.
Iran's economy was already suffering from major structural problems -- including major banking issues -- before Trump walked out of the nuclear deal.
But Trump's announcement in May helped fuel a run on Iran's currency that has seen the rial lose more than two thirds of its value, driving up prices and forcing the government to resort to food handouts for the country's poor. Rouhani came to power in 2013, vowing to rebuild ties with the world and attract billions of dollars in foreign investment.
The other parties to the nuclear deal -- Britain, France, Germany, China and Russia -- have all vehemently opposed the US move and vowed to keep trade going, though they are struggling to convince private companies to stand up to US pressure.
"Today, it's not just us who are angry with America's policies. Even European companies and governments are angry with America's policies," said Rouhani.
(This story has not been edited by Business Standard staff and is auto-generated from a syndicated feed.)