The deal was reached in July 2015 between Tehran and the six world powers of Britain, China, France, Germany, Russia and the US.
However, although Trump does not like the deal, his speech to the United Nations on Tuesday did not mean Washington would withdraw from the pact, Nikki Haley, US Ambassador to the UN, said on Wednesday.
Asked by CBS news whether Trump would withdraw the United States from the deal, the USA ambassador to the United Nations Nikki Haley said that was a decicion for the president alone.
MICHELE KELEMEN, BYLINE: For now the Trump administration has kept up its side of the bargain continuing to offer Iran sanctions relief in return for limits on Iran's nuclear program.
He gave his strongest hint to date in Tuesday's address that he would quit the accord by telling his fellow leaders that the "deal is an embarrassment to the United States, and I don't think you've heard the last of it".
"I explicitly announced at the United Nations that the JCPOA is a very important agreement, and we are determined to continue [implementing] it", May said during a meeting with Iranian President Hassan Rouhani in NY on Wednesday on the sidelines of the 72nd UN General Assembly session, according to the official website of the Iranian president. He singled out "the new USA administration" in saying it would destroy its own credibility by abrogating worldwide agreements.
"I want to stress that the Joint Comprehensive Plan of Action (JCPOA) is an important outcome of multilateralism", said Chinese Foreign Ministry spokesperson Lu Kang during a press conference.
Turning to the Israeli-Palestinian conflict, Rouhani said Iran never threatens anyone but also does not tolerate threats, adding that peace, security, stability and the progress of all nations are intertwined.
He cited Iran's support of Bashar al-Assad, engaging in cyber-warfare, conducting missile tests, and threatening United States ships in the region.
But Mr Tillerson said the talks were "very matter of fact", and acknowledged Iran was complying with the deal.
Mogherini specifically addressed that the USA would be handling Iran policy on its own outside of the JCPOA.