The move is Iran's latest step away from its nuclear deal with world powers since Trump withdrew from the accord over a year ago.
His speech at the U.N. General Assembly came shortly after U.S. Secretary of State Mike Pompeo announced new U.S. sanctions targeting Iran’s ability to sell its oil.
A centerpiece of this year's U.N. schedule will be a Monday session on climate change that Trump plans to skip.
Iran’s president Hassan Rouhani separately promised to unveil a regional peace plan at this week's upcoming high-level meetings at the United Nations.
Ayatollah Ali Khamenei's comments follow reports about a possible meeting between President Donald Trump and his Iranian counterpart, Hassan Rouhani.
“Americans have to realize that warmongering and warmongers are not to their benefit,” the Iranian president said in televised remarks.
Iran announced it has begun using advanced centrifuges to enrich uranium.
Donald Trump had said Monday at the G-7 that there's a "really good chance" that he and Hassan Rouhani could meet to discuss their nuclear impasse.
European leaders have struggled to calm the deepening confrontation between Iran and the United States since Trump pulled out of the 2015 nuclear deal.
The new threat comes days after President Hassan Rouhani said the nation could push its uranium enrichment level to "any any amount we want."
A diplomatic conflict between Tehran and Washington has flared since the U.S. pulled out of the 2015 Iranian nuclear deal.
President Hassan Rouhani threatened to do more if world powers didn't protect Iran from the impact of U.S. sanctions.
One year after threatening North Korea before the General Assembly, the U.S. president targets Iran.
President Hassan Rouhani claimed an unnamed U.S.-allied country was behind Saturday's attack.
Trump announced Monday that he would meet "anytime" with Iranian President Hassan Rouhani with "no preconditions."
But it's music to the ears of foreign policy hawks like John Bolton and Lindsey Graham.
"People are wondering why the president would threaten them with nuclear war, when he let Vladimir Putin practically run his fingers through his hair?"
"NEVER GONNA MAKE YOU CRY."
On Monday, the Iranian foreign minister warned Trump to "be cautious" -- echoing an earlier tweet penned by the U.S. president threatening Iran.
The comment comes after Iran's Hassan Rouhani said any conflict with his country would be "the mother of all wars."