He also challenged Ahmadinejad's reported denial of the Holocaust.
"When you come to a place like this it makes you simply ridiculous. The truth is that the Holocaust is the most documented event in human history."
Ahmadinejad rose to applause, and after a religious invocation said Bollinger's opening was "an insult to information and the knowledge of the audience here".
He blamed the university president's "unfriendly treatment" on the influence of the US media and politicians ahead of his visit.
"Many parts of his speech were insults," he said. "We actually respect our students and the professors by allowing them to make their own judgments."'Evil has landed'
Before his trip and during his Columbia speech and comments to the media on Monday, Ahmadinejad appeared to be reaching out to the American public, giving a much more balanced view than the US media has often portrayed.
On the Holocaust:
Why is it that the Palestinian people are paying the price for an event they had nothing to do with?
On Holocaust deniers:
My question was simple: There are researchers who want to approach the topic from a different perspective. Why are they put into prison? Why isn't it open to all forms of research?
On Israel as a Jewish state:
We are friends of all the nations. We are also friends with the Jewish people. There are many Jews in Iran living peacefully with security ... in our constitution and our laws and the parliamentary elections for every 150,000 people we get one representative in the parliament. For the Jewish community one-fifth of this number they still get one independent representative in the parliament... What we say is that to solve this 60-year problem, we must allow the Palestinian people to decide about its future for itself.
On nuclear research:
Some big powers create a monopoly over science and prevent other nations in achieving scientific development as well. This, too, is one of the surprises of our time. Some big powers do not want to see the progress of other societies and nations... Regretfully, they have not been trained to serve mankind.
If the root causes of 9/11 are examined properly - why it happened, what caused it, what were the conditions that led to it, who truly was involved, who was really involved - and put it all together to understand how to prevent the crisis in Iraq, fix the problem in Afghanistan and Iraq combined.
But even before his appearance at Columbia, the front page of New York's Daily News already ran the headline "The evil has landed" while The New York Post called Ahmadinejad the "Madman Iran Prez".
Thousands of people gathered outside the United Nations headquarters on Monday to protest against Ahmadinejad's visit.
The speakers, most of them politicians and officials from Jewish organisations, proclaimed their support for Israel and criticised the Iranian leader over remarks questioning the Holocaust.
"We're here today to send a message that there is never a reason to give a hatemonger an open stage," Christine Quinn, speaker of New York City's council, said.
Outside the university lecture hall where Ahmadinejad was to speak, several hundred protesters raised their objections to the event. Some linked arms and sang traditional Jewish folk songs about peace and brotherhood.
Inside, many students were wearing T-shirts with the message "Stop Ahmadinejad's Evil".Holocaust denial
Ahmadinejad rejected accusations that he has denied the Holocaust actually happened, but argued for more research to be conducted on the subject.
"I'm not saying that it didn't happen at all," he said. "I said, granted this happened, what does it have to do with the Palestinian people?"
He used his 30-minute speech to repeat Tehran's insistence that its nuclear programme was focused on meeting the country's electricity needs.
Washington says Iran is seeking to produce nuclear weapons.
"The countries that feel threatened ... should prepare for defence, and even counterattack"
Adolfo Talpalar, Stockholm, Sweden
Send us your views
"We do not believe in nuclear weapons. Period. This goes against the whole grain of humanity," Ahmadinejad said.
During the question-and-answer session he denied that homosexuals were persecuted in Iran.
"In Iran we do don't have homosexuals like in your country. In Iran we do not have this phenomenon. I do not know who has told you we have it," he said, sparking laughter from the audience.
Some, however, were not amused.
"This is a sick joke," said Scott Long of Human Rights Watch, saying Iran tortures gays under a penal code that punishes homosexuality between men with the death penalty.
US targets Iran force
Separately, Condoleezza Rice, the US secretary of state, ratcheted up the pressure on Tehran, telling the Reuters news agency that the US was considering sanctions against the entire al-Quds force of Iran's Revolutionary Guard.
Such a designation would enable Washington to target the force's financing.
The US accuses the Quds force of inciting violence in Iraq and of training and equipping fighters who have attacked US troops.
Iran has repeatedly denied this.
The US is increasing diplomatic pressure on Iran to stop uranium enrichment, which can produce nuclear weapons, and targeting the al-Quds force would be part of that strategy.
"Remember that the problem with the Quds force is that it has a network of activities in support of terrorism but it also, we believe, has a network of activities in support of proliferation," Rice said.