The disclosure on Thursday that Zohran Mamdani identified his race as both “Asian” and “Black or African American” as a high school senior applying to college has provoked sharply different reactions.

Three of his rivals in New York City’s mayoral race have strongly criticized Mr. Mamdani, with two suggesting potential fraud and calling for further investigation.

Right-wing pundits have flocked to social media to call Mr. Mamdani a liar — and worse.

And his supporters have rallied to his defense, angrily characterizing the disclosure as a politically motivated hit job with no bearing on the mayor’s race, one advanced by a right-wing academic who has promoted eugenic views.

The varied responses followed Mr. Mamdani’s acknowledgment on Thursday that he had “checked multiple boxes trying to capture the fullness of my background” while filling out an application to Columbia University in 2009. He said he had not been trying to gain an edge through Columbia’s race-conscious affirmative action admissions program — and, indeed, he was not accepted to the school.

The New York Times could find no speeches or interviews in which Mr. Mamdani referred to himself as Black or African American, and he said in an interview that applications to Columbia and other colleges were the only instances when he could recall describing himself as such.

Representative Ritchie Torres, a Bronx Democrat who endorsed Mr. Mamdani’s chief rival, former Gov. Andrew M. Cuomo, in the primary, said that he believed that, “within reason, we should all be the arbiters of our own identity.”