US President Donald Trump has threatened to abandon the agreement when it comes up for renewal on May 12, demanding his country's European allies "fix the terrible flaws" or he will re-impose sanctions.
"If the United States leaves the nuclear agreement, you will soon see that they will regret it like never before in history," Rouhani said in a televised speech in northwestern Iran.
"Trump must know that our people are united, the Zionist regime (Israel) must know that our people are united," Rouhani added.
The nuclear deal was struck in 2015 between Iran and Britain, China, France, Germany, Russia and the United States, then led by Barack Obama.
Under the pact, sanctions were lifted in return for a commitment not to pursue a nuclear bomb, but Iran says it is not reaping the rewards despite complying with the deal.
The Islamic republic has always denied it sought a nuclear weapon, insisting its atomic programme was for civilian purposes.
Rouhani did not specify how Iran would react if the US pulls out of the deal.
But he said he had given "the necessary orders", notably to Iran's Atomic Energy Organisation, in anticipation of Trump's decision.
On Thursday Ali Akbar Velayati, the foreign policy adviser to Iran's supreme leader Ayatollah Ali Khamenei, warned Tehran would quit the nuclear deal if the United States withdraws.
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