Britain, France and Germany - along with Russian Federation and China - had all pleaded unsuccessfully for President Donald Trump to remain in the six countries' 2015 accord with Iran on ending its nuclear programme.
"The Americans had no achievements in this public assembly", Rouhani said, at a news conference broadcast on state TV on his return to Tehran.
"Together, let us choose a future of patriotism, prosperity and pride", Trump said.
NEW YORK - Iran's president struck back at Donald Trump on Tuesday, hours after the United States leader delivered a speech castigating the foreign policy of the Islamic Republic.
"We have been informed that all European members of [the] Security Council intend to support the nuclear deal and stress the need for remaining committed to its implementation", Araqchi said.
Donald Trump, whose political ascent has been full of firsts, yesterday achieved another rare feat - bringing laughter to the solemn UN General Assembly. Trump says the deal was a "horrible" agreement that didn't do enough to contain Iranian "aggression".
"He'll call on every country to join our pressure campaign in order to thwart Iran's global torrent of destructive activity", said Pompeo.
From November, he said, USA sanctions would be in "full force" and the White House would impose further measures.
Rouhani also predicted that despite the Trump administration's departure from the nuclear deal in May, Washington would eventually come back.
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"Didn't expect that reaction, but that's OK", Trump said during the speech. Trump, who said this week he will have a second summit with Kim "quite soon", emphasized that Pyongyang has not tested a ballistic missile since the engagement process began early this year.
Instead, the entire General Assembly erupts into laughter.
Rouhani earlier said that as a precondition for any dialogue, Trump would need to fix the damage done by exiting the nuclear deal. "We don't want them to meddle or interfere in our upcoming election".
"We need a truly great leader, a genius at strategy and winning", tweeted Donald Trump back in 2014.
"Regrettably we found that China has been attempting to interfere in our upcoming 2018 election coming up in November against my administration", he said. He said the people of the Middle East had suffered "illegal invasion" in Iraq, the unjust overthrow of the Government in Libya in 2011, and a disastrous civil war in Syria - all the result of Western meddling.
"They learned how to synthesize them, they are building labs for that, and this is something we have been warned about for a long time".
For now, though, Rouhani made clear that Iran is not looking for a clash with the US.
Trump told the annual gathering: "They do not respect their neighbors or borders or the sovereign rights of nations".
"How can any nation that claims to sympathize with the people of Iran keep sustaining trading relationships with lawless and oppressive ayatollahs?"