In his speech to the UN, Trump said the deal - forged in 2015 between Iran and the USA, the UK, France, China, Russia, and Germany in a landmark bid to prevent Iran developing nuclear weapons - was "an embarrassment to the United States".
Nothing has changed other than the US response to North Korea.
He added that United States allies are looking "more carefully and seriously" at ways to push back against Iranian aggression. The European Union's foreign policy chief, Federica Mogherini, chairs the joint commission that is monitoring the deal's implementation.
"Frankly, that deal is an embarrassment to the United States, and I don't think you've heard the last of it - believe me", he declared.
Meanwhile, in a meeting between Zarif and Syrian Foreign Minister Walid al-Mualem, the two sides discussed the latest developments on Syria's political arena and the battlefield in the fight against terrorism and issues of common interest.
Crippling economic sanctions on Iran were lifted after the International Atomic Energy Agency certified Iran had restricted sensitive nuclear activities.
"One can nearly set the countdown clock to Iran resuming its nuclear activities", Tillerson said.
'By suggesting he would revisit and possibly cancel the Iran nuclear agreement, he greatly escalated the danger we face from both Iran and North Korea, ' she said in a statement.
"Whether we can agree, that's another thing", Tillerson said.
Several current or former U.S. politicians who favor a tougher stance on Iran also spoke, including independent former U.S. Sen. Trump and Netanyahu have said that Iran's missile advances and its military adventurism are also reasons to re-examine the Iran deal.
Nuclear tests feared in North Korea as a 3.4 magnitude quake detected
The Norway-based geological monitoring agency said the quake was likely caused by an aftershock rather than a new nuclear blast. North Korea's foreign minister later said that could be a hydrogen bomb test in the Pacific Ocean if Kim orders it.
Trump responded by threatening to unleash "fire and fury like the world has never seen" on North Korea if it continued to make threats against the U.S. But North Korea only continued to test more missiles. "And if you remember, Trump already said that the Iranians are not in compliance with the spirit of the deal and he said, frankly, they're probably not even in compliance with the actual deal".
President Trump has been more equivocal than predecessors about such a scenario, though senior aides say it remains the US goal.
Iranian President Hassan Rouhani told the General Assembly on Wednesday that Tehran is in compliance with its worldwide obligations and would not break them. "I thought it was very dark, dangerous, not the kind of message that the leader of the greatest nation in the world should be delivering", she said. This is - this is Secretary of State Rex Tillerson talking about the nuclear agreement, and this was yesterday on Fox News.
He stressed that "Iran does not seek to export the revolution by force of arms".
The nuclear issue, if unresolved, will create a more unsafe world "as other countries may follow the example of North Korea", he said.
Under the agreement, what must Iran do? "If he turns around in a month's time, in a few weeks' time and says they're not [compliant], what changed?"
They came a day after President Donald Trump denounced the deal. In return, the USA and the European Union will suspend nuclear-related sanctions against Iran, with the lifting of all past UN Security Council sanction resolutions.
In any event, the U.S.
"We would take a very different view of the nature of the North Korea agreement", Tillerson said, pointing out that there are few similarities between the two countries. She said all countries must "come together and defend the global order that we have worked so hard to create". So it's a very good deal that's made us more secure, made all of Iran's neighbors more secure.
A year ago, such a get-together would have been considered routine as nations strove to implement an agreement that curtailed Iran's nuclear activity in exchange for an end to various oil, trade and financial restrictions on the country.