Actor Chazz Palminteri apologized to Bill de Blasio during a heated, live radio exchange for calling the mayor’s wife a racist for nixing Italian American icon Mother Frances Cabrini in the “She Built NYC” competition to build statues of historic women.

“I would like you to tell your wife I apologize for saying — using the word racism again, I did not call her a racist but they asked me does this sound like racism to you and I did say, ‘Yes.’ As a man, I would not lie to you absolutely,” Palminteri told de Blasio during a WNYC call-in show Friday morning.

“Thank you for the apology and I’ll relay it to Chirlane,” the mayor said of his wife, Chirlane McCray, who headed the “She Built NYC” initiative.

“I will guarantee you another round of statues is coming and real soon, Mother Cabrini is right at the top of the list for consideration. I will make a strong case for Mother Cabrini,” the mayor said, calling the patron saint of immigrants a “stunning figure in history.”

The two Italian Americans’ kumbaya moment came after the “A Bronx Tale” actor initially defended his remarks in a long and testy exchange with the mayor on 77 WABC radio last week.

“Absolutely, she is being racist,” the actor said when asked about McCray’s decision to ignore a city poll that put Cabrini at the top of a list for female statues.

When Palminteri called in to the mayor’s regular WNYC appearance Friday, de Blasio asked him if he’d really called McCray a racist or if his remarks were “misreported by the New York Post.” The paper covered the WABC exchange.

“You’re live on the radio. The New York Post says you called my wife — who is a tremendous public servant who loves people of all backgrounds, who named her children Chiara and Dante and honors their Italian heritage — that you called her a racist. I can’t believe you would have done that, but I’m sure you’ll tell me the honest truth,” de Blasio said.

“I will tell you the honest truth, I was asked a question, ‘Do you think that is racism?’ and I did say the word ‘Yes.’ I did not call her a racist,” Palminteri said.

“At the least,” he said, the Cabrini snub showed “bias.”

De Blasio ripped into his paisano.

“You don’t call someone a racist who isn’t a racist, it just isn’t factually right and it’s inappropriate and it’s unfair,” the mayor fumed.

“I said and they asked me, ‘Is that racism?’ and I said, ‘It looks like it,'” Palminteri shot back.

“Except it isn’t, it isn’t, and I would urge people not to use that term where it doesn’t exist,” the mayor argued. “What my wife has done is expect people of all races throughout her life. Everything she’s done is about everyone. There’s not an ounce of racism there.”

As Palminteri repeatedly tried to interject, host Brian Lehrer asked the actor if he wanted to retract his statement. At first, he demurred.

“I would just like if it wasn’t that I would just like the answer of how a woman who could have done so much be considered for the next round when she should have been in the first round,” Palminteri explained.

But that remark set Hizzoner off on another tirade.

“That has nothing to do with race, for God’s sake!” de Blasio thundered. “I would have welcomed a call, for you to pick up the God damn phone and say, ‘Hey, a lot of us think this is a great idea. Can we make this happen?’ and I would have said, ‘That’s a great idea, let’s get to work on it.’

“I would urge you to be a little more respectful,” de Blasio added.

Palminteri wasn’t ready to give up.

“To be fair, if it was the other way around, you don’t think, you don’t think the African American community would have jumped up and said something if you just totally disregarded someone like Rosa Parks,” Palminteri said.

That’s when Lehrer asked the actor again if he wanted to apologize and he finally said he was sorry.

Just hours after the WNYC interview, Palminteri told The Post the jury is out on whether his exchange with de Blasio was productive. The mayor told the actor-playwright hat he would recommend that a statue be dedicated to Cabrini during the next round of “She Built NYC” selections.

“We’ll see if I made headway. The proof is in the pudding now. Mother Cabrini has to get a statue,” Palminteri said.

But Palminteri, who earlier apologized to the mayor for calling McCray racist over the Cabrini snub, backpedaled a bit in the Post interview. “I manned up for something I said. But if it wasn’t racism or bias, what was it?,” he said.