Live on Iranian television the President savaged President Trump and said the agreement would not be renegotiated and Iran's ballistic missile programme will EXPAND despite pressure from the United States.
Mr Rouhani said President Trump's speech was full of "insults and fake accusations" against Iran.
He said: "The Iranian nation has not and will never bow to any foreign pressure…Iran and the deal are stronger than ever … Iran's Islamic Revolutionary Guards Corps will continue its fight against regional terrorists."
"The great nation of Iran saw tonight once again that America took a hostile position against an international deal.
"Once again, the [European Union] also took a firm position against the United States. America is now more than ever isolated."
The USA refused to certify Tehran is complying with the deal, which was negotiated during Barack Obama’s reign and aimed to keep Iran's nuclear programme under control.
The 2015 agreement lifted stiff sanctions against Iran that had been in place for decades in exchange for significant restrictions on the nation's nuclear program.
It signals a more confrontational approach to Iran from Mr Trump, who has reluctantly rectified the deal twice despite concerns about loopholes.
He said this evening: “History has shown that the longer we ignore a threat the more dangerous it become.”
The Iranian President has slammed President Trump
He described Iran as a “rogue regime” responsible for “hostile actions”.
Mr Trump said Iran will “never – and I mean never” achieve nuclear status.
He said Iran was “the world’s leading state sponsor of terrorism” and linked them to the Taliban, Hezbollah and Hamas.
Mr Trump also said: “It threatens American ships and threatens freedom of navigation. It launches cyber attacks against our critical infrastructure and military.
“The regime violently suppressesesses its own citizens. This regime has fuelled sectarian violence in Ira and vicious civil wars in Yemen and Syria."
President Trump refused to recertify the deal
Earlier today a top Iranian general threatened to BURY Donald Trump after his threats against Iran's international nuclear deal.
The commander of Iran’s Quds Force, the overseas arm of the Islamic Revolutionary Guards Corps (IRGC) said that the powerful forces has “buried many” like the US President.
He also said that President Trump’s threats against the Gulf nation would “damage” America.
Speaking to Tasnim news agency, Quds commander, Brigadier-General Esmail Ghaani said: “We are not a war-mongering country.
But any military action against Iran will be regretted … Trump's threats against Iran will damage America … We have buried many … like Trump and know how to fight against America.”
- BRINK OF WAR: Europeans hatch plan as Trump braced to axe Iran deal
- World War 3 fears as Russia sends missiles to Saudi Arabia
- Iran warns Trump will spark global chaos if US pulls out of deal