Rouhani downplayed the sharp words from the USA administration, including a warning Tuesday by Trump's national security advisor, John Bolton, that Iran would have "hell to pay" if it crosses the United States.
Trump who had called Rouhani "an absolutely lovely man", in a tweet earlier on Tuesday, described Iran in his speech as "a corrupt dictatorship, whose leaders sew chaos, death and disruption".
Seated at the center of an arc-shaped table, Trump immediately uttered tough words against Iran, saying that a government with Iran's track record "must never be allowed to obtain" a nuclear weapon.
On the Syria conflict, he said the USA would respond if chemical weapons are used by the Assad regime in Syria.
He added that since the deal was signed, the "pathways of the signatories of the JCPOA have diverged.but we still, all of us here, retain the same objective of preventing Iran from obtaining nuclear weapons, and guaranteeing strict worldwide control on the peaceful use of their nuclear programme".
He again promoted the ideals of isolationism while also laying into nations like Iran, for its perceived aggression towards the United States, and China, for its continuing role in what Trump has labelled an out-and-out trade war.
On Wednesday, Trump is set to lead a U.N. Security Council meeting on Iran and the non-proliferation of nuclear weapons.
But the assembly nonetheless laughed out loud at the idea that Trump has led an effective presidency.
"While President Obama whitewashed the behavior of Iran in an attempt to create the appearance that it is a peace-loving, reasonable country in order to forge the nuclear deal, the actual behavior of Iran since agreeing to the deal has been antithetical to that", Stern told JNS.
Trump added, "So true".
Only US President Donald Trump, who chaired the session, spoke against the deal known as the JCPOA and appeared isolated as a result, Rouhani said. We do not wish to attack them.
Trump insisted at a Wednesday news conference that he started grinning and foreign counterparts chimed in with laughter.
In a furious speech to the UN Security Council, Mr Trump said the United States would pursue "tougher than ever before" sanctions against the Islamic Republic.
With US-China trade tensions only getting worse, Mr Trump suggested his much-touted friendship with President Xi Jinping was coming to an end and accused Beijing of interfering in the upcoming US mid-term elections.
"The president delivered a powerful indictment of Iran's destabilizing role in the Middle East, and slammed biased United Nations groups that castigate America and Israel", said Richard Goldberg, a senior adviser at the Foundation for Defense of Democracies.
Leftist Bolivian President Evo Morales bluntly declared that "the United States does not care about human rights or justice".