In his General Assembly speech, Rouhani targeted Trump in language if not directly in name.
That meeting turned, instead, into a strong show of support for the 2015 multilateral nuclear deal with Iran, which the Trump administration scrapped in May in defiance of the very same council's Resolution 2231, said Rouhani.
US-Iran relations have been sour for decades and Mr Trump has rarely lost an opportunity to criticise Tehran.
"What Iran says - concluded its president - is clear: no war, no sanctions, no threats, no pressure, act only in accordance with the law and to respect obligations".
In the aftermath of Donald Trump's announcement to withdraw from the landmark deal curbing Iran's nuclear programme, the leaders of Britain, France and Germany who signed the agreement published a joint statement, saying they will continue to stick by it.
Dr Pieper, of the University of Salford, said: "During his address at the UN General Assembly, Iranian president Rouhani said the illusion "should be cast away that one can aspire to securing more peace and security at the cost of denying others peace and security".
Turning to Syria, Trump assailed Russian Federation and Iran for backing President Bashar la-Assad in his brutal war in Syria, saying: "The Syrian regime's butchery is enabled by Russian Federation and Iran".
Heading into the council meeting, Sweden's Foreign Minister Margot Wallstrom said European Union governments will "stand up" for the nuclear deal and suggested the USA approach would fail. The country's behavior will be a major focus on Wednesday when Trump leads a meeting of the U.N. Security Council. "It is pure fiction", he said, according to ABC News. In addition, a few leaders prodded Trump on the US withdrawing from the Paris Agreement as part of the United Nations Framework Convention on Climate Change.
"We do not and will not interfere in any country's domestic affairs", said Foreign Minister Wang Yi.
Trump told the Security Council that "many things are happening behind the scenes" between the United States and North Korea as they pursue denuclearization of the Korean Peninsula.
Earlier Wednesday, Trump said his administration is planning a second summit with Kim and details will be announced soon.
President Donald Trump will hold a news conference at 5 p.m. on Wednesday, following the United Nations General Assembly in New York City.
The White House said no meeting was planned between the two leaders, and Venezuela's information ministry did not respond to a request for comment. Trump added, "So true".