In a televised speech, Rouhani said the “Iranian government will react firmly” if the White House fails to “live up to their commitments” under the agreement.
The warning comes weeks in advance of a May 12 deadline for Trump to renew the deal.
The US president has previously said he would scrap the Joint Comprehensive Plan of Action (JCPOA), which he has called the “worst deal in history”, unless “a better option” is presented to him.
International leaders have called on Trump to uphold the agreement. On Sunday, French President Emmanuel Macron said there was no “Plan B” if Trump decided to pull out.
“Is this agreement perfect and this JCPOA a perfect thing for our relationship with Iran? No. But for nuclear – what do you have? As a better option? I don’t see it,” Macron said.
In an interview with US broadcaster CBS aired on Sunday, Iranian Foreign Minister Mohammad Javad Zarif said that Iran could consider “resuming at much greater speed” their nuclear activities if the US were to pull out.
The landmark deal reached in Lausanne, Switzerland in April 2015 with China, Russia, France, Great Britain, Germany and the US offered Iran more than $110bn a year in sanctions relief and a return to the global economy in exchange for halting its drive for a nuclear weapon.