The NYPD’s rank and file reacted with fury Thursday at being “thrown under the bus” by Mayor Bill de Blasio, who said he and First Lady Chirlane McCray had trained their mixed-race son, Dante, about the “dangers” posed by cops.

Pat Lynch, president of the Patrolmen’s Benevolent Association, blasted de Blasio for his inflammatory remarks, which followed Wednesday’s decision by a Staten Island grand jury not to indict cop Daniel Pantaleo in the chokehold death of Eric Garner.

“What police officers felt yesterday after that press conference was that they were thrown under the bus,” Lynch said.

De Blasio had called the Garner case “profoundly personal for me,” saying that because of “the dangers [Dante] may face, we’ve had to literally train him . . . in how to take special care in any encounter he has with the police officers who are there to protect him.”

The comments angered cops, with one saying, “Did he tell his son to be wary of his police bodyguards, that he should be afraid of them as they pick him up at school and drive him where he needs to go?”

Lynch railed that de Blasio effectively told New Yorkers to teach their kids “that they should be afraid of New York City police officers.”

“That’s not true!” Lynch shouted. “Our city is safe because of police officers. All of our sons and daughters walk the streets in safety because of police officers. They should be afraid of the criminals. That’s what we should be teaching.”

In other developments tied to the grand jury’s decision:

A judge granted Staten Island DA Dan Donovan’s request to unseal information about the grand jury proceedings, including that the panel heard from 50 witnesses, watched four videos and was told how much force cops can legally use in arrests.

Police Commissioner Bill Bratton said the NYPD was “moving forward” with a departmental investigation of the cops in Garner’s fatal July 17 arrest, with interviews starting Friday.

Bratton also backtracked on his initial assessment that cellphone video showed Pantaleo applying a banned chokehold, telling CNN, “I’ve been around a long time in this business. What appears to be sometimes may not be what it is.”

Gov. Andrew Cuomo said the state should consider appointing a special prosecutor to handle cases of alleged police brutality. “We have a problem. Let’s acknowledge it,” he told CNN.

Meanwhile, Pantaleo’s lawyer revealed that other cops at the scene of the arrest told the grand jury his client had tried to get Garner to comply with orders — which wasn’t caught on video.

“Let’s make this easy. You’ve been through this before,” Pantaleo told Garner, according to his lawyer, Stuart London.

London also told the Associated Press that Pantaleo admitted hearing Garner say “I can’t breathe” after being taken down, but believed that once Garner was on the ground, paramedics could revive him.

Pantaleo testified that he “used a takedown move and any contact to the neck was incidental,” the lawyer added.

London told The New York Times that Pantaleo feared for his life as he grappled with the 350-pound Garner in front of a shop’s plate-glass storefront.

“He testified that the glass buckled while Garner was up against him and he was against the glass,” he said. “He was concerned that both he and Garner would go through that glass.”

After the grand jury decision, President Obama said he had phoned de Blasio and “commended him for his words.”

Christopher Sadowski Christopher Sadowski Protesters march in Lincoln Center on Dec. 3. Christopher Sadowski Christopher Sadowski Christopher Sadowski Christopher Sadowski People blocking the Lincoln Tunnel argue with police as they protest. Reuters New York City police officers block people from marching into the Lincoln Tunnel. EPA Natan Dvir People protest in midtown Manhattan after it was announced that the New York City police officer involved in the death of Eric Garner is not being indicted. Natan Dvir Protesters face off with police officers in Times Square during a city-wide protest. EPA Marchers sit in the street at Seventh Avenue and 42nd Street in Times Square during the protest. EPA Protesters, demanding justice for the death of Eric Garner, disrupt traffic along the West Side Highway. Reuters Protesters, demanding justice for the death of Eric Garner, disrupt traffic along the West Side Highway. Reuters Protesters in Times Square head to Rockefeller Center to protest the grand jury decision not to indict Police Officer Daniel Pantaleo in the death of Eric Garner. David McGlynn A group of protesters with signs rally against the decision not to indict the police officer involved in the death of Eric Garner as they mix with spectators near Rockefeller Center during a ceremony to light the Rockefeller Center Christmas tree. AP AP Police stand guard near Radio City Music Hall. AP David McGlynn David McGlynn David McGlynn Protesters gather in Times Square on Dec. 3 to protest the grand jury decision not to indict Police Officer Daniel Pantaleo in the death of Eric Garner. Robert Mecea Robert Mecea William Farrington David McGlynn David McGlynn David McGlynn Protesters lie on the floor of Grand Central Station. Getty Images EPA Protester Linder Hampton wears a shirt reading "I can't breathe" as she speaks to reporters in Staten Island. AP Two women hug near the site of Eric Garner's death in Staten Island after it was announced that the officer involved in his death is not being indicted. AP A man yells and chants slogans near the site of Eric Garner's death. AP Ad Up Next Close Woman 'stole' $60K in jewelry and cash in ritual to banish spirits A female charlatan scammed a Chinatown woman out $60,000 worth... 32 View Slideshow Back Continue Share this: Facebook

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But city cops had a markedly different reaction.

“What a f- -king idiot. I listened for about two minutes, and then I was done,” one said.

Another cop said de Blasio “is fanning the fires more than anyone else in this city by not coming out in favor of the police officers who work for him.”

Former Mayor Rudy Giuliani lashed out at de Blasio’s claim that reaction to the grand jury decision was fueled by “centuries of racism.”

“This helps to create this atmosphere of protest and even sometimes violence. There was no racism in this case,” Giuliani told “Fox and Friends.”

At a news conference Thursday to announce a $35 million “retraining” of the NYPD’s 22,000 street cops, de Blasio tried to eat some of his words.

Asked about his implication that young black men should fear the NYPD, de Blasio insisted, “That’s not what I said.”

“I said there is a history and there is a reality that a lot of people feel fear. It’s not that they should, it’s that they do, and we have to address it and we have to be honest about it,” he said at the new Police Academy in Queens.

Additional reporting by Natalie Musumeci, Michael Gartland and Carl Campanile

Chokehold cop’s fate unknown

The fate of NYPD Officer Daniel Pantaleo will be hanging in the balance for quite some time while federal authorities decide whether to file civil-rights charges against him in the death of Eric Garner, law-enforcement sources told The Post Thursday.

US Attorney General Eric Holder and his nominated successor, Brooklyn US Attorney Loretta Lynch, both vowed a swift probe.

But sources noted similar promises following the 2008 acquittal of three NYPD cops who killed Sean Bell. The feds took two years before announcing there would be no civil-rights charges.

Reported by Selim Algar, Jamie ­Schram and Bruce Golding

Boehner open to hearing

WASHINGTON — House Speaker John Boehner opened the door Thursday to congressional hearings on “unanswered questions” in the deaths of Michael Brown and Eric Garner.

“There are a lot of unanswered questions that the Americans have and, frankly, I have,” Boehner (R-Ohio) said at an unrelated press conference.

On the possibility of House inquiry into the cases, he said: “I’m not going to rule that in or out.”

Reported by Marisa Schultz