The president separately told reporters he had made up his mind on whether to leave the Iranian denuclearization pact that he has long said was poorly brokered by his predecessor Barack Obama - but he would not disclose his position.
In his speech to the UN, Trump said the deal - forged in 2015 between Iran and the U.S., the UK, France, China, Russia, and Germany in a landmark bid to prevent Iran developing nuclear weapons - was "an embarrassment to the United States".
Elsewhere in the meeting, Zarif pointed to the crisis in the Korean Peninsula and said, "We reject any production, test and development of nuclear weapons".
European Union foreign policy chief Federica Mogherini put the bravest possible face on the encounter, stressing that Iran and the major powers agree the deal is "delivering".
Iran says it has the right to nuclear energy and insists its nuclear programme is for peaceful purposes only.
"There are countries that accuse Iran of destabilizing the region in order to increase its sales of weapons", Rowhani said.
He condemned Washington's "verbosity, especially the very insolent remarks by the president of the country". Bolton's strategy calls for an end to the JCPOA and in its place new sanctions to permanently stop Iran from possessing nuclear technology.
He reiterated that the exit of the USA from such an agreement would carry a high cost, meaning that subsequent to such an action by the United States of America, no one will trust America again.More news: Small quake hits North Korea in 'suspected explosion'
In particular, he objects to the "sunset clause" that would see Iran resume some enrichment from 2025.
"I think the time has come for a decision to be made", Tillerson added.
"We are the same people who rescued the Jews from Babylonian servility", he said, referring to the Jewish communities established in Persia after they wer expelled by the Babylonians from Judea in the sixth century BCE.
French President Emmanuel Macron also pushed back on Trump's efforts to undo the accord.
European diplomats, while sharing those concerns, are becoming exasperated by the argument - insisting the accord was designed exclusively to stop Iran getting the bomb.
Assembly delegates are still reeling from Trump's threat to "totally destroy" North Korea, and if America is blamed for tanking the Iran deal, Trump may find it hard to cajole Kim Jong-Un into a diplomatic solution.
As Congress faces a possible fight over the future of the Iran nuclear agreement, senior Senate Democrats demanded on Wednesday that the Trump administration provide lawmakers with any information showing Tehran is not complying with the global pact. "We definitely do not need to go into another one", she said.
What does the United States do?More news: Shifty Maria could prompt storm watch here by tomorrow
Russian Foreign Minister Sergei Lavrov reaffirmed Russia's commitment to maintaining the sustainability of the Joint Comprehensive Plan of Action (JCPOA) on the Iranian nuclear program, TASS reported.
BLINKEN: In an ideal world, we would have negotiated every misbehavior that Iran conducts both at home and around the world.
In his address to the UN General Assembly, the president on Tuesday called the nuclear deal "an embarrassment" for the United States and Tillerson later confirmed that the agreement must be "revisited".
Until the matter was resolved the U.S. would fulfil its commitments, he said.
"It was not an angry tone at all".
What's in the agreement and why does it matter? "I sense that we're on the cusp of something very special, the scale of the opportunities is really quite extraordinary".
ABC10 reached out to local expert on American Foreign Policy and International Relations, Dr. David Andersen-Rodgers, to get a deeper look at the significance of Trump's words. The secretary told reporters it would now take some time to prepare to implement the decisions.More news: North Korea's Kim Jong-Un, Trump Threats Worry Russia
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