In repeated clashes with his hosts, Mr. Ahmadinejad accused the United States of supporting terrorist groups, and characterized as hypocritical American and European efforts to rein in Iran’s nuclear ambitions.

“If you have created the fifth generation of atomic bombs and are testing them already, who are you to question other people who just want nuclear power,” Mr. Ahmadinejad said, adding, pointedly: “I think the politicians who are after atomic bombs, politically, they’re backwards. Retarded.”

His speech at Columbia, in advance of his planned speech today at the United Nations, produced a day of intense protests and counterprotests around the campus. It was a performance at once both defiant — he said Iran could not recognize Israel “because it is based on ethnic discrimination, occupation and usurpation and it consistently threatens its neighbors” — and conciliatory — he said he wanted to visit ground zero to “show my respect” for what he called “a tragic event.”

And he said that even if the Holocaust did occur, the Palestinians should not pay the price for it.

He began the afternoon on the defensive.

Lee C. Bollinger, the president of Columbia, under intense attack for the invitation — one protester outside the campus auditorium where Mr. Ahmadinejad spoke passed out fliers that said, “Bollinger, too bad bin Laden is not available” — opened the event with a 10-minute verbal assault.

He said, “Mr. President, you exhibit all the signs of a petty and cruel dictator,” adding, “You are either brazenly provocative or astonishingly uneducated.”

The Iranian president, who was seated 10 feet away from him on the stage, wore a frozen smile. The anti-Ahmadinejad portion of the audience, which looked to be about 70 percent of it, cheered and chortled.

Mr. Bollinger praised himself and Columbia for showing they believed in freedom of speech by inviting the Iranian president, then continued his attack. He said it was “well documented” that Iran was a state sponsor of terrorism, accused Iran of fighting a proxy war against the United States in Iraq and questioned why Iran has refused “to adhere to the international standards” of disclosure for its nuclear program.

“I doubt,” Mr. Bollinger concluded, “that you will have the intellectual courage to answer these questions.”

Mr. Ahmadinejad did not directly answer the questions, but he did address them. Before doing so though, he said pointedly:

“In Iran, tradition requires when you invite a person to be a speaker, we actually respect our students enough to allow them to make their own judgment, and don’t think it’s necessary before the speech is even given to come in with a series of complaints to provide vaccination to the students and faculty.”

He added, to some cheers, “Nonetheless, I shall not begin by being affected by this unfriendly treatment.”

Mr. Ahmadinejad’s much-talked-about appearance at Columbia was the opening act of a week of dramatic theater here as the United Nations General Assembly opened its annual session. He and his nemesis, President Bush, are scheduled to address the General Assembly today.

Mr. Bush, asked about Columbia’s decision to invite Mr. Ahmadinejad, told Fox News that it was “O.K. with me,” but added that he might not have extended the invitation himself.

“When you really think about it,” Mr. Bush said, “he’s the head of a state sponsor of terror, he’s — and yet an institution in our country gives him a chance to express his point of view, which really speaks to the freedoms of the country. I’m not sure I’d have offered the same invitation.”

Mr. Ahmadinejad is allowed under international law and diplomatic protocols to travel freely within a 25-mile radius of Columbus Circle. But the police said last week that he would not be allowed near ground zero.

Inside the auditorium, the Columbia students laughed appreciatively when Mr. Ahmadinejad pushed back against the attempts by Dean John H. Coatsworth, the event’s moderator, to get him to stop rambling and answer questions directly.

“Do you or your government seek the destruction of the state of Israel?” Mr. Coatsworth asked.

“We love all people,” Mr. Ahmadinejad dodged. “We are friends of the Jews. There are many Jews living peacefully in Iran.” He went on to say that the Palestinian “nation” should be allowed a referendum to decide its own future.

Mr. Coatsworth persisted: “I think you can answer that question with a simple yes or no.”

Mr. Ahmadinejad was having none of it. “You ask the question and then you want the answer the way you want to hear it,” he shot back. “I ask you, is the Palestinian issue not a question of international importance? Please tell me yes or no.”

For that, he got a round of applause from the students, who had lined up four hours before the speech to get into the auditorium. Online tickets evaporated in 90 minutes last week, they said, almost on par with a Bruce Springsteen concert.

“I’m proud of my university today,” said Stina Reksten, a 28-year-old graduate student from Norway. “I don’t want to confuse the very dire human rights situation in Iran with the issue here, which is freedom of speech. This is about academic freedom.”

It remains unclear whether Columbia’s leaders were able to mollify critics through their critical treatment of Mr. Ahmadinejad. But they made some headway: the American Israel Public Affairs Committee sent out an e-mail message shortly after the speech with the subject line, “A Must Read: Columbia University President’s Intro of Iran’s Ahmadinejad today.”