Trump has long decried past US leaders - especially his predecessor, Barack Obama - for showing weakness on the world stage.
When President Barack Obama was in the White House, Trump was often critical of his approach to foreign affairs and routinely claimed that the world was laughing at the U.S. because of Obama's leadership.
"The United States stands ready to export our abundant affordable supply of oil, clean coal, and natural gas", Trump told the United Nations General Assembly. "We will examine what is working, what is not working, and whether the countries who receive our dollars and our protection also have our interests at heart". Following more laughter, Trump said, "Didn't expect that reaction, but that's okay".
Rouhani earlier said that as a precondition for any dialogue, Trump would need to fix the damage done by exiting the nuclear deal.
"US President Donald Trump evoked laughter at the UN General Assembly as he boasted about his administration's accomplishments in his speech".
In that speech, he called North Korean leader Kim Jong Un "Rocket Man" and warned that the US would "have no choice but to totally destroy" the rogue nuclear nation if Kim continued on his "suicide mission".
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Iranian soldiers take shelter during a terror attack in a military parade in Ahvaz, Iran , Sept. 22, 2018. Ramazan Sharif told ISNA that an Arab separatist group carried out the attack, without elaborating.
"We will never surrender America's sovereignty to an unelected, unaccountable global bureaucracy", he said.
Trump blasted what he called the "corrupt dictatorship" of Iran and accused the government in Tehran of spreading "mayhem" across the Middle East and around the world.
He said that preventing Iran from exporting oil would be "very unsafe".
He also used the speech to insist the US was stronger and richer than when he took office almost two years ago.
Mr. Kim requested a second meeting with Mr. Trump in a letter this month, and Mr. Trump said, "we will be doing that".
Mr Rouhani invited the United States to return to the negotiating table and said a dialogue does not have to mean a photo opportunity.