Iranian President Mahmoud Ahmadinejad on Monday questioned why Iran can't have a nuclear program when the United States has one, repeated his inference that historical accounts of the Holocaust are myths, and denied that there are homosexuals in Iran.

In animated remarks before students and faculty at a controversial speaking engagment at Columbia university, the Iranian leader also denied that Iran sponsors terror, and instead pointed the finger at the U.S. government as a supporter of terrorism.

"We don't need to resort to terrorism. We've been victims of terrorism, ourselves," he said. "Within six months, over 4,000 Iranians lost their lives, assassinated by terrorist groups. All this carried out by the hand of one single terrorist group. Regretfully, that same terrorist group now, today, in your country, is operating under the support of the U.S. administration, working freely, distributing declarations freely, and their camps in Iraq are supported by the U.S. government."

Ahmadinejad did not name the group to which he was referring.

• Click here to view photos of Ahmadinejad's New York visit.

Columbia President Lee Bollinger opened the program with a blistering introduction in which he lambasted Ahmadinejad for calling for the annihilation of Israel, denying the Holocaust and supporting the execution of children, and told the leader of Iran that he resembled "a petty and cruel dictator."

Bollinger levied repeated criticisms against Ahmadinejad, calling on him to answer a series of challenges about his leadership, blasting his views about the "myth" of the Holocaust as being "absurd," and saying that he doubted he "will have the intellectual courage to answer these questions."

"You are either brazenly provocative or astonishingly uneducated," Bollinger told Ahmadinejad about the leader's Holocaust denial. "Will you cease this outrage?"

After sitting through Bollinger's rebuke, Ahmadinejad rose to applause, and after a religious invocation, opened his remarks by objecting to the scolding, saying it was insulting to be spoken about that way.

"At the outset, I want to complain a bit about the person who read this political statement made against me," Ahmadinejad said. "In Iran, we don't think it's necessary to come in before the speech has already begun with a series of complaints ... It was an insult to information and the knowledge of the audience here."

He said Bollinger's speech was full of "insults and claims that were incorrect, regretfully," and accused Bollinger of offering "unfriendly treatment" under the influence of the U.S. press and politicians.

He did not address Bollinger's accusations directly, instead launching into a long religious discussion laced with quotes from the Koran before turning to criticism of the Bush administration and past American governments, from warrantless wiretapping to the bombing of Hiroshima and Nagasaki.

He asked why the United States was allowed to develop nuclear weapons capabilities, but his country was not.

"How come you have that right and we don’t have it?" he challenged.

On the issue of the Holocaust, Ahmadinejad said more "research" was needed on what took place, but he seemed to acknowledge that it did exist.

"I am not saying that it didn't happen at all. This is not that judgment that I am passing here," he said. "Granted this happened, what does it have to do with the Palestinian people? ... Why is it that the Palestinian people are paying the price for an event they had nothing to do with?"

And the Iranian leader denied that homosexuality exists in his country when asked to explain the execution of homosexuals in Iran.

"In Iran we don't have homosexuals like in your country," he said, to laughter and boos from the audience. 'In Iran we do not have this phenomenon. I don't know who's told you that we have this."

Ahmadinejad began the first full day of his controversial New York City trip Monday--his third in three years-- amid mounting protests and air-tight security, with his first appearance beginning just after noon EDT via video before the National Press Club in Washington, D.C. His highly publicized visit to Columbia University in New York City began at 1:30 p.m.

Bollinger, who was strongly criticized for inviting Ahmadinejad to Columbia, had promised tough questions in his introduction to Ahmadinejad's talk, but the strident and personal nature of his attack on the president of Iran was startling.

"Mr. President, you exhibit all the signs of a petty and cruel dictator," Bollinger said, to loud applause.

He said Ahmadinejad's denial of the Holocaust might fool the illiterate and ignorant.

"When you come to a place like this it makes you simply ridiculous," Bollinger said. "The truth is that the Holocaust is the most documented event in human history."

Ahmadinejad said he simply wanted more research on the Holocaust, which he said was abused as a justification for Israeli mistreatment of the Palestinians.

"Why is it that the Palestinian people are paying the price for an event they had nothing to do with?" Ahmadinejad asked. He closed his prepared remarks with a terse smile, to applause and boos, before taking questions from the audience.

During the question and answer period, Ahmadinejad was taken to task on remarks he has made calling for the destruction of Israel, with the Columbia moderator accusing him of failing to answer the question.

"We love all nations. We are friends with the Jewish people. There are many Jews living in Iran with security," Ahmadinejad said. "Our proposal to the Palestinian plight is a humanitarian and a democratic proposal. What we say is that to solve this 60-year problem, we must allow the Palestinian people to decide about its future for itself."

The moderator asked him to simply answer "yes" or "no" on whether or not he wanted to destroy Israel.

"Mr. President, I think many members of our audience would like to hear a clearer answer to that question," the moderator said. "The question is: Do you or your government seek the destruction of the state of Israel as a Jewish state? And I think you could answer that question with a single word, either yes or no."

"You asked the question, and then you want the answer the way you want to hear it. Well, this isn't really a free flow of information," Ahmadinejad retorted. 'I'm just telling you what my position is. I'm asking you: Is the Palestinian issue not an international issue of prominence or not? Please tell me, yes or no? There's the plight of a people."

The moderator told him the answer to his question was "yes," and the Iranian president thanked him for his cooperation.

"We recognize there's a problem there that's been going on for 60 years. Everybody provides a solution. And our solution is a free referendum," the Iranian president said. "Let this referendum happen, and then you'll see what the results are."

Ahmadinejad said he believes that the United States and Iran have the potential to be great friends.

"I think that if the U.S. administration, if the U.S. government, puts aside some of its old behaviors, it can actually be a good friend for the Iranian people, for the Iranian nation," Ahmadinejad said.

"If the U.S. government recognizes the rights of the Iranian people, respects all nations and extends a hand of friendship with all Iranians, they, too, will see that Iranians will be one of its best friends."

President Bush said Ahmadinejad's appearance spoke to the "greatness" of the United States of America.

"He's the head of a state sponsor of terror, and yet, an institution in our country gives him the chance to express his point of view, which really speaks to the freedoms of the country," Bush told FOX News on Monday ahead of the Columbia event. "I'm not so sure I'd offer the same invitation, but nevertheless, it speaks volumes about the greatness, really, of America. We're confident enough to let a person express his views. I just really hope he tells everybody the truth."

Bush said that while he's "not sure" he would have offered the Iranian leader a platform from which to outline his agenda, he thinks it's OK that Columbia University did invite Ahmadinejad to speak.

"This is a place of high learning and if the president (of Columbia) thinks it's a good idea to have the leader from Iran come and talk to the students as an educational experience, I guess it's OK with me," Bush told FOX News in an interview. "The problem is Ahmadinejad uses these platforms to advance his agenda, which I suspect in this case ... He doesn't want America to know his true intentions."

Before his Columbia appearance Monday, the Iranian leader, speaking via video from New York City to journalists at the National Press Club in Washington, D.C., tossed aside a question about Israel by saying Iran doesn't recognize the "regime," accusing it of killing people and committing various other atrocities.

It was typical of many of Ahmadinejad's responses, which often started with laughing challenges to journalists in which he said, "That's not right," or asked, "Where are you getting that?"

The Iranian president started his speech at the Press Club by reciting some verses from the Koran. No one on the panel or seated in the audience applauded or reacted in any way when he was introduced.

On the Holocaust — which the Iranian leader has called a "myth" — he said that "if the Holocaust is a reality, why don't we let more research be done on it? ... Where did the Holocaust happen to begin with? It happened in Europe, and given that, why is it that the Palestinian people should be displaced? Why should they give up their land?"

He also defended his request to visit Ground Zero--the site of the Sept. 11, 2001, attacks on New York City--saying he wanted to "pay my respects." But, he claimed, the U.S. government and other politicians prevented that from happening.

"I was interested in expressing my sympathy to victims of tragedy," he said. "It's the responsibility of everyone to understand the root causes of 9/11."

His request to lay a wreath at ground zero was denied by city officials and condemned by politicians who said a visit to the site of the 2001 terror attacks would violate sacred ground.

Police cited construction and security concerns in denying Ahmadinejad's request. Ahmadinejad told "60 Minutes" he would not press the issue but expressed disbelief that the visit would offend Americans.

During the Press Club address, the Iranian president delivered some remarks through an interpreter and then answered questions from the moderator. A similar format was used at the Columbia event.

Ahmadinejad said the world needs to build a better future "based on peace and security of all humanity," and he spoke of a world full of love, kindness, beauty and allegiance to God as the ultimate goal.

"No one should prevent love and kindness from flourishing in mankind and turn it into hostility," the Iranian president said. "Family is the center of love and beauty."

He said people should follow God, who would lead them to a "sublime" state.

"When we take a look around us, we are not happy with what we see," Ahmadinejad said. "Threats of war have affected everyone. Continuous wars have in fact hurt the human spirit. If we look at the root cause of some of these problems, we will be able to think about how to build a better future, a more prosperous future based on peace and security of all humanity."

Ahmadinejad spoke of the importance of the press, in spite of the fact that Iran's media is state-run and criticized as tightly controlled by the government.

"The press plays a connecting role. It provides information and can serve as a channel for promoting current thinking," he said. "The role of the press is to disseminate moral behavior ... The press can be the voices of the divine prophets."

The Press Club moderator asked the Iranian leader about Iranian weapons and involvement in Iraq, about his views on whether religions other than Islam have a place in the world, and on his country's treatment of women and approach to the freedom of the press.

The Iranian president repeatedly asked where the moderator got his information and challenged the truth of his statements.

And when asked whether Iran was sending weapons into Iraq to fight against American troops, Ahmadinejad replied that "Iraq security means our security." When pressed, he denied that Iran was engaging in that kind of activity.

When asked whether he wanted to go to war, he said he did not.

"Why is there a need for war?" Ahmadinejad said. "Why should they threaten another country? Why should they create more insecurity? I think officials who talk this kind of talk should really be pressured and warn to know what to say and when not to say something."

Ahmadinejad said that the religions of "Christ and Moses" as well as Islam are "all brothers. They all want the same thing."

He defended Iranian women as among the most free in the world, and said they were involved in all walks of life in Iran.

Thousands of people jammed two blocks of 47th Street across from the United Nations Monday to protest Ahmadinejad's visit to New York. Organizers claimed a turnout of tens of thousands. Police did not immediately have a crowd estimate.

The speakers, most of them politicians and officials from Jewish organizations, proclaimed their support for Israel and criticized the Iranian leader for his 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," New York City Council Speaker Christine Quinn said.

Protesters also assembled at Columbia. Dozens stood near the lecture hall where Ahmadinejad was scheduled to speak, linking arms and singing traditional Jewish folk songs about peace and brotherhood, while nearby a two-person band played "You Are My Sunshine."

Signs in the crowd displayed a range of messages, including one that read "We refuse to choose between Islamic fundamentalism and American imperialism."

Ahmadinejad said Monday in an interview with The Associated Press that Iran would not launch an attack on Israel or any other nation.

"Iran will not attack any country," Ahmadinejad told the AP. Iran has always maintained a defensive policy, not an offensive one, he said, and has "never sought to expand its territory."

Asked whether he believed the U.S. is preparing for war with Iran, he responded: "That is not how I see it ... I believe that some of the talk in this regard arises first of all from anger. Secondly, it serves the electoral purposes domestically in this country. Third, it serves as a cover for policy failures over Iraq."

In a 30-minute interview at a hotel near the United Nations, Ahmadinejad struck a soothing tone. He said Iranian foreign policy was based on humanitarian concerns and seeking justice.

He reiterated his call for a debate at the United Nations on world issues with President Bush.

Referring to fears of a military campaign against Iran, he said: "We don't think you can compensate for one mistake by committing more mistakes."

Ahmadinejad's scheduled address to the U.N. General Assembly on Tuesday was to be his third time attending the New York meeting in three years. The New York City police and the U.S. Secret Service are charged with providing a security detail and protecting the Iranian leader along with dozens of heads of state arriving for the assembly.

The Iranian mission has not disclosed Ahmadinejad's specific itinerary.

FOX News' Catherine Donaldson-Evans and The Associated Press contributed to this report.