As the president of Iran, Mahmoud Ahmadinejad, prepares to address Columbia University today amid a storm of student protest, state and city lawmakers say they are considering withholding public funds from the school to protest its decision to invite the leader to campus.

In an interview with The New York Sun, the speaker of the Assembly, Sheldon Silver, said lawmakers, outraged over Columbia’s insistence on allowing the Iranian president to speak at its World Leaders Forum, would consider reducing capital aid and other financial assistance to the school.

Lawmakers warned about other consequences for Columbia and its president, Lee Bollinger, who has resisted campus and public pressure to cancel Mr. Ahmadinejad’s appearance today, arguing that Columbia’s commitment to scholarship requires the school to directly confront offensive ideas.

“There are issues that Columbia may have before us that obviously this cavalier attitude would be something that people would recall,” Mr. Silver said. “Obviously, there’s some degree of capital support that has been provided to Columbia in the past. These are things people might take a different view of … knowing that this is that kind of an institution.”

Mr. Silver faulted Columbia for “attempting to legitimize this individual,” saying, “We have an obligation because of the U.N. to allow him to come to this country. It doesn’t mean we have to make him welcome. We don’t have to give him a forum.”

The speaker said he was infuriated by comments made on Saturday by the acting dean of the School of International and Public Affairs, John Coatsworth, who said in a television interview that it would have been proper for Columbia to extend a speaking invitation to Hitler in 1939. Mr. Coatsworth’s school is sponsoring the event.

“What makes it more outrageous is the fact that some dean yesterday said he would have invited Adolf Hitler. It’s totally outrageous. This is not a matter of academic freedom. This is a matter of legitimizing people, one who was the perpetrator of the Holocaust and one who denies its existence,” Mr. Silver said.

“He’s clearly responsible for the deaths of Americans both in Iraq and elsewhere. And he remains as much a threat to the world as anybody today. I don’t understand what this dean and Columbia are thinking,” Mr. Silver said.

Mr. Silver’s criticism of Columbia was echoed by other elected officials, who argued that Columbia was lending its name and prestige to a leader of a terrorist-sponsoring dictatorship who denies the existence of the Holocaust, vows to eliminate Israel, preaches Islamic extremism, and aspires to build nuclear weapons.

“Bollinger made a big mistake, and there should be consequences for him for making that decision,” the chairman of the New York City Council’s Finance Committee, David Weprin, said in an interview. “We should look at everything involving Columbia, whether it be capital projects, city and state, or other related things that we do in the city for them,” he said.

Mr. Weprin was one of several elected officials who joined Jewish leaders, Columbia students, and alumni yesterday at a demonstration at the Morningside Heights campus to protest Mr. Ahmadinejad’s talk.

“It’s not going to go away just because this episode ends. Columbia University has to know … that they will be penalized,” an assemblyman of Brooklyn, Dov Hikind, who also attended the rally, said. The lawmaker said Mr. Ahmadinejad should be arrested when he sets foot on campus.

Speaking at the rally, a New York City Council member, James Gennaro, urged university donors to withhold their dollars from the institution, while Rep. Anthony Weiner, a potential mayoral candidate in 2009, said Columbia’s reputation was taking a “brutal beating.”

Mr. Silver’s warning of sanctions against Columbia is a highly unusual departure for a state leader who has seldom, if ever, threatened to use the power of the state purse to punish a private university.

A spokesman for the Senate Republicans, John McArdle, said the majority conference is “going to review the whole situation and decide on how, or whether, to proceed.”

Mayor Bloomberg, who visited the Flight 93 memorial site in Shanksville, Pa., yesterday told reporters he disagreed with Columbia’s decision to host Mr. Ahmadinejad but promised the city would “provide the protection to make sure that when he gets there, he speaks safely without any threats and leaves.”

Albany awards Columbia millions of dollars a year in student financial aid and also provides funding for smaller-scale capital projects. Last year, Albany awarded the school $10 million for nanotechnology center and $12 million for a cancer center in Washington Heights.

Columbia uses the state Dormitory Authority to borrow money at low interest rates. Mr. Silver could use his influence over the authority to weed out Columbia bonding projects before they are submitted for approval.

The school is also seeking approval from city lawmakers for its plan to expand into a 17-acre swath of land in West Harlem. Albany also has the power to use eminent domain to facilitate Columbia’s expansion.

Mr. Bollinger has defended his university’s invitation to Mr. Ahmadinejad, saying that in order to fulfill Columbia’s mission, he must respect the rights of faculty and deans to “create programming for academic purposes.” On occasion, he said, “this will bring us into contact with beliefs many, most, or even all of us will find offensive and even odious.”

A year ago, Mr. Bollinger rescinded Columbia’s invitation to Mr. Ahmadinejad to speak at the same annual forum, apparently overruling a former dean of SIPA, Lisa Anderson. Mr. Bollinger, at the time, said he couldn’t be certain that the Iranian leader’s presence at the school would “reflect the academic values that are the hallmark of a university event such as our World Leaders Forum.” An assistant to Ms. Anderson said the event was cancelled because of security and logistical concerns.

Inside the university, Mr. Bollinger yesterday faced criticism from several student leaders, some of whom supported the invitation to Mr. Ahmadinejad but said they were angry that they were not consulted by the administration.

“I’ve heard a lot of feedback already from people saying they don’t want to give money,” Elizabeth Goldhirsch, who graduated from Columbia’s school of journalism in 2002, said. “I will not make a donation if this stance is maintained.”

Mr. Bollinger, who has served as president since 2002, also was confronting signs of increasing division in his administration.

The dean of Columbia Law School, David Schizer, in a statement called Mr. Ahmadinejad “a reprehensible and dangerous figure,” and said it would be “deeply regrettable if some misread this invitation as lending prestige or legitimacy to his views.”

Mr. Ahmadinejad, who is attending the U.N. General Assembly, arrived in New York late yesterday. He is scheduled to speak at Columbia for an hour, beginning at 1:30 p.m., and will issue his remarks in Farsi with simultaneous translation, a university spokesman said.

Columbia officials say the Iranian leader will be escorted onto campus through the gate at 114th Street, which leads directly to Lerner Hall. He is scheduled to depart immediately after the event. Campus security, which is coordinating with local and federal authorities, is planning for more than 10,000 protesters to congregate outside the university’s gates.

Columbia distributed 600 tickets to the talk, where Mr. Ahmadinejad will field questions from Mr. Bollinger as well as faculty and students. The event is to be broadcast on televisions and lounges across campus.

Mr. Bollinger said in a statement that he would question the Iranian president on human rights issues, as well as his position that Israel should be “wiped off the map” and that the Holocaust did not occur.