Chazz Palminteri, the actor who this month accused Mayor de Blasio’s wife of being “a racist,” picked up the telephone on Friday morning and called in to a radio show where the mayor was fielding questions.

The mayor, it appeared, also had something to say.

“I want you to keep Chazz on the line,” the mayor said to the show’s host, Brian Lehrer of WNYC, “because I think there’s something we have to set the record straight on.”

What followed was a debate about what happens when race, ethnicity and the legacies of prominent figures collide in 2019.

Mr. Palminteri had been upset that the mayor’s wife, Chirlane McCray, who is black, did not embrace an effort to honor Mother Cabrini, America’s first saint and a hero to Italian-Americans, with a statue. Ms. McCray leads the city’s effort to erect new monuments in the city.