How is Mayor de Blasio going to defuse the tension with the New York Police Department? Mayor Giuliani is urging him to apologize for giving the impression that he sided with protesters against the deaths black men who have — here and elsewhere —died at the hands of police. “I said it day one,” Mr. Giuliani declared on “Face the Nation” on CBS “and I think he’d get this over with if he did it.”

We’re not so sure it’s going to be all that easy. Certainly an apology is in order for the things Mr. de Blasio said in the wake of the death of Eric Garner and amid the protests over the more general issue of police killings of African American men. But what about the sense of betrayal that the mayor has managed, in but a year in office, to instill in New York’s Finest. Police are the department that is the most basic in the executive of any government.

Mr. de Blasio, after all, was in trouble with the police and their union even before the death of Eric Garner on Staten Island. He was in trouble with the police before he was sworn into office. This owes to the nature of his campaign against the stop-question-and-frisk police tactics. His very campaign for the mayoralty put him on the side of the plaintiffs in a lawsuit that sought to smear the integrity of the entire patrol.

Remember, stop question and frisk was originally brought by individual plaintiffs — David Floyd, first among them — who felt they were wrongly stopped by police. We’ve never had a problem with such a lawsuit, and the courts are the right place to get down to individual cases. But the lawsuit was transmogrified into a class action for all minority New Yorkers.

It became, moreover, a suit not just against the individual officers who had arrested the plaintiffs but against the whole force and its leadership. It sought to brand the police force and its leadership as racists intent on violating our civil rights laws. How could this not be widely resented among the men and women in blue? Particularly because it’s inaccurate. It’s just not how the officers who patrol our streets think of themselves.

So New York’s Finest had reason to expect the city would defend them. Not just because of the risks they breast every day but because it’s a serious matter to be branded as a racist. This is one of the reasons that Mayor Bloomberg — to his everlasting credit — mounted such a spirited defense against the class action in Floyd. The mayor was right on the merits, and it was their responsibility as leaders.

The judges who ride the Second United States Appeals Circuit certainly gave Mr. de Blasio an opening shortly before he was to take office. They tossed off the case the United States District Judge who ruled against the police. The court said that the judge, Shira Scheindlin, had failed to maintain the required appearance of impartiality. That would have been the moment for Mr. de Blasio to take a hint.

He could have backed the police in court, even while easing up on the use of stop-and-frisk tactics. Commissioner Bratton had been widely criticizing the way Commissioner Kelly had overseen the program. It was the prerogative of the new mayor to adjust the program and see how it correlated with crime. Meantime Mr. de Blasio could have appealed to overturn Judge Scheindlin’s ruling against the police as a class.

Instead, Mr. de Blasio did the most polarizing possible thing. He had the city switch sides in the case, drop the appeal of Judge Scheindlin’s ruling, and enter settlement talks that would brand the police as racists. It would set the stage for a payout of vast legal fees that yet may be used to fund more attacks on the police. And it would leave a sense among the Finest that their own civilian leadership was against them.

At that point it was only the police unions who stepped up. They did their best to be permitted to represent the police where the city wouldn’t. That principle had been granted a few years back to the union representing the officers of Los Angeles Police Department. But the Second Circuit concluded that in New York the unions had waited too long. How this situation can now be rescued we don’t know, but our guess is that an apology won’t suffice. It wouldn’t surprise us if it has to wait for the next election.