Iranian President Mahmoud Ahmadinejad has clashed with the head of New York's Columbia University while making his controversial appearance at the campus.
Mr Ahmadinejad said Iran was "a peaceful nation"
Columbia President Lee Bollinger described Mr Ahmadinejad as a "cruel dictator" who denied the Holocaust.
In response, Mr Ahmadinejad called the remarks "an insult", adding that more research was needed on the Holocaust.
He again defended Tehran's nuclear ambitions and said it had every right to pursue a peaceful programme.
Washington accuses Iran of seeking to build a nuclear bomb and arming insurgents in Iraq - Tehran rejects the accusations.
Many Americans said the Iranian leader should not have been invited to speak at Columbia University.
But his appearance was popular - crowds flocked to a large screen set up on university grounds, and tickets to the actual event were quickly snapped up.
Mr Ahmadinejad's appearance sparked protests in New York, with demonstrators saying it provided a platform for hate.
Mr Ahmadinejad has been denied a visit to the site of the 11 September attacks in New York in 2001, with US Secretary of State Condoleezza Rice saying that "it would have been a travesty".
"This is somebody who is the president of a country that is probably the greatest sponsor - state sponsor - of terrorism," Ms Rice told CNBC television.
Mr Ahmadinejad was invited to Columbia University to address its students at the university's World Leaders Forum.
He received a hostile welcome from Mr Bollinger, who described the Iranian leader as "a petty and cruel dictator".
"You are either brazenly provocative or astonishingly uneducated," Mr Bollinger told Mr Ahmadinejad, referring to his denial of the Holocaust.
In response, Mr Ahmadinejad said that Mr Bollinger's remarks were "an insult to information and the knowledge of the audience".
The BBC's Jon Leyne, in New York, said Mr Ahmadinejad was visibly annoyed. At one point he demanded to know why raising issues about the Holocaust or the existence of Israel was not compatible with freedom of speech, our correspondent says.
Mr Ahmadinejad has called in the past for an end to the Israeli state and described the Holocaust as a "myth".
Addressing the Holocaust issue, Mr Ahmadinejad said he simply wanted more research to be done.
He also said the issue was abused by Israel to justify what he said was its mistreatment of the Palestinians.
'Evil has landed'
Asked about executions of homosexuals in Iran, Mr Ahmadinejad replied: "In Iran we don't have homosexuals like in your country."
Reacting to laughter and jeers from the audience he added: "In Iran we don't have this phenomenon, I don't know who told you this."
The New York Daily News's front page headline on Monday read "The Evil Has Landed", while the New York Post described Mr Ahmadinejad as "Madman Iran Prez".
Dozens of protesters gathered outside the university on Sunday, but Mr Bollinger defended the university's invitation, saying it was a question of free speech and academic freedom.
The Iranian leader is in New York to attend the UN General Assembly, where he is due to speak on Tuesday.
Our correspondent says Mr Ahmadinejad firmly believes he can convince global opinion and the American people of the rightness of his cause.