Trump defended his decision to exit the 2015 Iranian nuclear accord signed under his predecessor Barack Obama and said that a USA campaign of "economic pressure" would turn back Islamic Republic's aggression.
His visit to Pyongyang next month will be his fourth this year.
In his UN address previous year, Trump bashed the nuclear deal as "an embarrassment", signalling that the United States was ready to walk away.
"Iran's leaders sow chaos, death and destruction", Trump said.
The US President said that Tehran's leaders "do not respect their neighbours or borders or the sovereign rights of nations".
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"It is ironic that the USA government does not even hide its plan for overthrowing the same government it invites to talks", Rouhani said in a speech at the United Nations General Assembly.
Secretary of State Mike Pompeo accepted an invitation from North Korea on Wednesday to return to Pyongyang next month, a sign that denuclearization talks will resume after President Trump canceled a meeting last month citing a "lack of progress".
US President Donald Trump says the United Nations wasn't laughing at him when he boasted about his government's successes during a speech to world diplomats.
He dismissed such concerns, saying a declaration would only be a political or symbolic gesture aimed at providing some security assurances to the North, which agreed to give up its nuclear weapons in exchange for security guarantees from the U.S. "We had fun. That was not laughing at me".
"Chairman Kim Jong-un is a young but very honest and frank person, and I am convinced he has a firm determination to denuclearize", the president said when asked about his impression of the North Korean leader.
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The world's two largest economic superpowers have already applied tariffs on $50 billion of each other's imports. Other retailers, including Target, also spoke out against tariffs, saying they will "hurt American consumers".
"We must encourage North Korea to stay on the path that leads to permanent and solid peace", he said.
Asked later about what intervention he might be considering in Venezuela, Trump said he's looking very strongly at the possibility, given the awful things happening there.
Also, the president said a declaration of war's end could be reversed at any time if necessary while the denuclearization steps taken or will be taken by North Korea cannot.
Asked by CBS if Kim had agreed to allow global inspectors into nuclear sites, Pompeo said, "Yes", while adding that verification was important in any nuclear agreement. "We'll begin the work of resolving conflicts in northeast Asia, starting from the Korean peninsula".
To facilitate the process, Moon said the United States should reciprocate North Korea's goodwill gestures toward denuclearization.
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Pompeo also confirmed to CBS that Kim would be allowing inspectors into nuclear testing sites as part of the commitment made to the United States.