In a televised address during a cabinet meeting Sunday evening, Rouhani warned, "if the U.S. wants to engage in bullying, it will face Iran's rigid response," state-run Islamic Republic News Agency reported.
Rouhani described the yearlong effort to re-impose the sanctions not only as a defeat for the Trump administration but one that has isolated the United States on the diplomatic stage.
"From now on, what the United States speaks about means nothing but rebellion, and no one will accept it, and the consequences of such words and such positions will go back to the United States itself," Rouhani said, according to a summary of the meeting published by his office.
Despite international pushback, the Trump administration on Saturday said it reimposed U.N. sanctions against Iran that were removed following the 2015 nuclear deal. The sanctions include extending an arms embargo.
"The United States expects all U.N. Member States to fully comply with their obligations to implement these measures," U.S. Secretary of State Mike Pompeo said in a statement Saturday night.
Pompeo has said the United States can re-impose the sanctions despite no longer being a party to the nuclear deal, as it is a U.N. member and can invoke the so-called snapback mechanism in Resolution 2231 that recognizes the deal also signed by China, France, Germany, Russia, Britain and the European Union.
President Donald Trump called the Obama-era deal "defective at its core" when he withdrew the United States in 2018. Iran has since violated some provisions of the pact.
Pompeo, who initiated a 30-day deadline for the sanctions to go into effect, threatened consequences for nations that don't comply with sanctions that are designed so that Iran "does not reap the benefits of U.N.-prohibited activity."
Pompeo said the return of sanctions will make the world safer and is "a step toward international peace and security," describing Iran as the greatest threat to peace in the Middle East.
Majid Takht Ravanchi, Iran's ambassador to the U.N., responded that the U.S. claim to the snapback mechanism is "null & void," as it is no longer a party to the nuclear deal.
Iran's foreign ministry said in a statement Sunday the U.S. move is "groundless and invalid and lacks any legal effect," and accuses Pompeo of trying to intimidate other nations into compliance.
Britain, France and Germany rejected the snapback claim.
"It flows from this that any decisions and actions, which would be taken based on this procedure or on its possible outcome, would also be incapable of having any legal effect," the nations said in a joint statement. "We have worked tirelessly to preserve the nuclear agreement and remain committed to do so."
U.S.-Iran tensions have risen since Trump's withdrawal from the deal, resulting in several maritime skirmishes and a U.S. drone strike early this year that killed Islamic Revolutionary Guard Corps commander Gen. Qassem Soleimani.