Rudolph W. Giuliani, the former mayor who shepherded New York City through the Sept. 11 attacks, said on Sunday that he did not think Mayor Zohran Mamdani should attend memorial ceremonies this week to mark the 25th anniversary of the attacks.

“It offends me,” Mr. Giuliani said in an anti-Muslim diatribe on the far-right news outlet Newsmax, regarding Mr. Mamdani plans to attend the New York memorial. Mr. Giuliani also compared Mr. Mamdani to the Sept. 11 hijackers, who he said had hostility to America and “they weren’t hiding it like Mamdani is trying to hide it.”

Mr. Giuliani’s tirade also included baseless claims, including that Mr. Mamdani is a supporter of a Muslim plot that aimed at “taking over certain parts of America and certain parts of Europe,” a right-wing conspiracy theory he has endorsed in the past.

His comments on Sunday made him the most prominent person to endorse a call from some conservatives for Mr. Mamdani to skip this week’s memorial ceremonies.

That demand has also been the subject of an online petition, which by Sunday had drawn almost 100,000 signatures.

Mr. Mamdani’s office declined on Sunday to directly address Mr. Giuliani’s comments, but directed reporters to his response to that online petition.

“I will proudly honor the families, the survivors, the first responders forever impacted by that horrific terror attack by standing alongside them at this year’s 9/11 commemoration, reaffirming that we will never forget the solemn day felt by all of us who call this city home and, frankly, by all of us who call this country home,” the mayor’s statement said.

The mayor’s office also pointed to two executive orders he signed last week to establish Sept. 11 as an annual “Citywide Day of Remembrance and Service” and to take steps to modernize the city’s emergency preparedness procedures.

According to his schedule, Mr. Mamdani has already attended or plans to attend roughly a dozen Sept. 11 memorial events, primarily at firehouses across the city that had been the home stations for firefighters who died in the attack or developed illnesses in its aftermath.

Earlier this year, Mr. Giuliani was hospitalized with a serious case of pneumonia and said he believed his health problems stemmed in part from exposure to airborne toxins that blanketed parts of the city after the collapse of the World Trade Center.

Mr. Giuliani was two blocks away from the first tower when it collapsed, and his head and shoulders were dusted with ash from the disaster as he joined the throngs of people fleeing north through Lower Manhattan.

Mr. Mamdani was 9 years old and in class at his Upper West Side elementary school when the attacks took place. He has spoken about the attacks as a formative experience for him as a child.

In an interview with The New York Times last year, he spoke of how important it is “to honor the memories of those that were killed” and described “learning their stories over the many years that I’ve been a New Yorker, the deep sorrow, that continues to this day, of futures that were stolen from so many and families that continue to live with that.”

He also talked about how Islamophobic backlash to the attacks had made anti-Muslim prejudice “a fact of life” for Muslim Americans.

“It was this horrific day that was also for many New Yorkers the moment at which they were marked an ‘other,’” he said.

Mr. Giuliani was widely praised and seen as a unifying figure after Sept. 11 for his stoic response to the attacks, which killed more than 2,700 people in New York City and left parts of Manhattan devastated for years.

But in the years since, Mr. Giuliani has politically drifted far to the right, serving as a high- profile surrogate and personal attorney for President Donald J. Trump. Last year, Mr. Trump pardoned Mr. Giuliani and several others who had been accused of trying to overturn the results of the 2020 presidential election.