The comments were made by Bruno Le Maire, French economy minister, during an interview with the Financial Times.
He claimed: “Europe refuses to allow the US to be the trade policeman of the world.”
President Trump pulled the US out of the nuclear deal Mr Obama signed with Iran in 2015 and has reimposed a range of economic sanctions.
He has repeatedly threatened punitive action against any European companies which ignore these sanctions and continue doing business with Iran.
Mr Le Maire argued the US measures threaten the EU’s “economic sovereignty” and urged the bloc to “affirm our independence”.
He added European countries will push ahead with plans to create a new financial channel to bypass US sanctions on Iran, allowing European firms to continue their current trading with the state.
After the first round of US sanctions were reinstated in August Trump tweeted: “Anyone doing business with Iran will not be doing business with the United States.”
A second round of sanctions, predominantly targeting Iran’s crucial oil industry, came into effect later this month.
Most European countries strongly opposed President Trump’s decision to withdraw from the Iran nuclear deal, designed to prevent the theocratic state acquiring nuclear weapons, in May of this year.
The UK, Germany and France released a joint statement in response expressing “regret and concern” and announcing they would continue to honour the deal.
Trump claimed the Iran deal, which he dubbed “the worst deal ever”, was failing to stop Iran from developing advanced missiles or backing terror groups across the Middle East.
Russia has also condemned the reimposition of sanctions, and vowed to circumvent them.
The country’s foreign minister, Sergey Lavrov, accused the US of deploying “unacceptable methods” while Turkish President Recep Tayyip said Washington’s actions “contradict the norms of international law”.
Mr Le Maire’s comments come just days after French President Emmanuel Macron controversially claimed the US could be a threat to European security.
Speaking to Europe 1 Radio he argued: “We have to protect ourselves with respect to China, Russia and ever the United States of America.”
He went on to urge the creation of a “true, European army”.