Mr Trump also boasted that his administration had accomplished "more than nearly any" other in USA history.
His words were greeted with laughter but he laughed back, saying: "Didn't expect that reaction".
As for the rest of the speech, Trump took aim at Iran, calling it a "corrupt dictatorship" that is plundering the Iranian people to pay for aggression overseas.
Even though top Trump officials say that there is no plan for regime change in Iran, their disdain and contempt for the leadership in Tehran has rarely been more palpable. "They do not respect their neighbors or borders or the sovereign rights of nations".
A year ago, Trump stood at the worldwide rostrum and derided the North Korean leader as "Little Rocket Man" and threatened to "totally destroy North Korea".
In his address previous year to the UN, Trump insulted Kim as a "rocket man" bent on nuclear destruction.
"What Iran says is clear: no war, no sanctions, no threats, no bullying; just acting according to the law and the fulfilment of obligations", Rouhani said.
He also asked, "all nations to isolate Iran's regime as long as it continues".
"It was a different world", Trump said Monday of his one-time moniker for Kim Jong Un.
"The new deal that we hope to be able to sign with Iran, and it will not be a personal agreement between two governments like the last one, we seek a treaty", Hook said in a speech last week. He received a stay of punishment at least until Thursday, when he is to meet with Trump at the White House.
Iran is a major focus of the annual week of United Nations diplomacy, months after Trump irritated U.S. allies in Europe by withdrawing from a 2015 agreement under which Tehran has sharply curtailed its nuclear program in return for sanctions relief.
The US President ran a bit late for his once-a-year speech at the UN General Assembly, forcing organisers to change the order of speakers. Rouhani told CNN he had not requested a bilateral meeting with the USA president.
Iranian President Hassan Rouhani has accused the United States of trying to overthrow his government, rejecting bilateral talks after U.S. counterpart Donald Trump predicted stepped-up sanctions would get Tehran to negotiate over its nuclear programme.
The Tuesday morning speech at United Nations headquarters in New York City also touched on improving relations with North Korea and the escalating trade war with China.
Trump said in July he was ready to meet Iran's President Hassan Rohani without preconditions to negotiate a new deal.
This after the United States announced tariffs recently on another $200 billion in Chinese-made goods for a total, so far, of $250 billion.
Trump has been busy enough at the United Nations that he hasn't had time to tweet about the speech, but once he gets back in to the warmer comforts of his couch, he'll surely let rip with what will no doubt be a tirade for the ages.