Iran's president Hassan Rouhani has said the United States will eventually rejoin the global nuclear deal President Donald Trump quit earlier this year.
The official topic of the gathering is billed as the "non-proliferation of weapons of mass destruction".
"Iran's leaders sow chaos, death and destruction", Trump told the gathering in the green-marbled hall.
"Today I stand before the United Nations General Assembly to share the extraordinary progress we've made".
"We reject the ideology of globalism", Trump said.
"In the years since the deal was signed, Iran's aggression only increased", Trump said.
An expert with the National Iranian American Council expressed a similar sentiment following Mr Trump's speech.
But his calls for other countries to join USA sanctions against Tehran were rejected by the other signatories of the 2015 nuclear deal with Iran - Britain, France, Russia, China, and Germany.
Paul Pogba: Alexis Sanchez will deliver at Manchester United
So it is a match of 90 minutes which we have to try and win and the choice of the players is based on that. Maybe as well we felt a bit of fatigue because we played Champions League [against Young Boys].
At the onset of the gathering, former Senator Joe Lieberman (D-Conn.) was given an Iranian coin by United Against Nuclear Iran's (UANI) CEO Mark Wallace to commemorate, what they hoped would be, the impending collapse of the regime.
"I do not accept the erosion of multilateralism and don't accept our history unraveling", Macron told the assembly, at times raising his voice.
"Didn't expect that reaction, but that's OK", Trump said during the speech.
Pompeo criticized the European Union's intention to establish a work-around to USA sanctions, while Bolton warned of "hell to pay" if Iran continued aggravating other nations.
President Donald Trump said he would present a two-state peace plan for the Middle East in the coming months, voicing confidence the Palestinians would return to talks despite his unwavering support for Israel.
On North Korea, Trump called for sanctions to be strictly enforced against Pyongyang - a message directed at Russian Federation and China which are pushing for an easing of punitive measures to reward North Korean leader Kim Jong Un.
But Macron said he was convinced that they all "retain the same objective in mind - namely, preventing Iran from obtaining nuclear weapons and guaranteeing strict worldwide control on the peaceful use of their nuclear program".
Mr Trump chose to pull the USA from the Iran deal, and defended that decision on Tuesday during his speech to the UN. He called on OPEC to stop raising oil prices and criticised China's trade practices.