And in an uncharacteristically public salvo, Police Commissioner James P. O’Neill took to Twitter to sharply criticize Vance’s decision not to charge one of the men, Sydney Williams, 37, and not to seek bail on the second, Aaron Grissom, 36.

O’Neill said Vance’s handling of the matter put the safety of police officers and the public in jeopardy and sent the wrong message to New Yorkers.

During a radio interview with Joe Piscopo later in the day, O’Neill defended the officers’ actions, saying the violence had started when Grissom refused to be arrested and punched one of the police officers. “You can’t punch a cop,” he said. “You can’t fight a cop. You can’t resist arrest. You have to respect the police.”

Vance declined to respond to O’Neill’s criticisms. “Our office is conducting a full, fair and independent investigation into the alleged offenses for which Mr. Grissom and Mr. Williams were arrested,” Danny Frost, the district attorney’s spokesman, said. “We are separately conducting a full, fair and independent investigation into the force used by officers during this encounter.”

The police commissioner’s comments underscored the simmering tensions between the two law enforcement agencies. Though they historically have been closely aligned, Vance and the district attorneys in Brooklyn and the Bronx have met resistance from the Police Department as they have embraced more liberal policies, like not prosecuting all low-level arrests for marijuana possession and farebeating.

Still, over his two-year tenure, O’Neill has rarely clashed openly with Vance, even when other high-ranking members of his department were accusing Vance’s office of mismanaging the investigation into allegations of sexual misconduct against Hollywood producer Harvey Weinstein.

The brawl in Washington Heights erupted Tuesday afternoon after police officers — identified in court documents as Jeffrey Mota and Bramlin Rosa — asked Williams and Grissom to leave the subway entrance at 169th Street and Broadway after complaints from riders that the men were smoking on the stairs, police said.

In a six-minute video taken by a passer-by and posted to Instagram, police are seen pummeling Grissom with batons and kicking him.

In a separate video obtained from a nearby bodega, which police released, Grissom can be seen just before the Instagram video swinging at the police officers as they back across the street.

The incident has prompted an internal affairs investigation into accusations of excessive force, though O’Neill pushed back against that allegation Friday morning.

“What I’m seeing right now, and this is preliminary results, these cops did exactly what we asked them to do,” he said in the radio interview.

Williams and Grissom were arrested and charged with felony assault. But when they were brought before a judge Thursday evening, prosecutors deferred charges against Williams, who had been struck in the head with a baton early in the video. He was released. Grissom was charged with assault, attempted assault and resisting arrest, but prosecutors did not ask for bail and he was also released.

Police said the men were arrested in the same station last month on charges they attacked police officers with fists and a baseball bat. They were charged with resisting arrest and drug possession.

In a Facebook video, first reported by The Daily News, Williams boasted that he had filed multiple lawsuits against police in the past after rough arrests. “They get hurt and I get paid,” he said.

O’Neill said, “He’s a serial resister, and when it’s over, he sues the Police Department.”

Sanford Rubenstein, a lawyer for Williams and Grissom, said they planned to sue the city over the arrest.

“The Manhattan DA’s office needs to wake up and realize that police officers cannot do our job when prosecutors won’t do theirs,” said Patrick J. Lynch, president of the Patrolmen’s Benevolent Association, which represents the city’s police officers. “Every perp who has ever thought about taking a swing at a cop is watching the outcome in this case.”

The incident has created a politically difficult situation for Mayor Bill de Blasio, who ran as a criminal justice reformer and has gone through periods of conflict with police. He said Wednesday that he was concerned about the beating Grissom suffered at the hands of officers in the video. He now finds himself walking a fine line between his police commissioner and the Manhattan district attorney.

“It is absolutely unacceptable to hit a cop or to resist arrest,” Olivia Lapeyrolerie, a spokeswoman for de Blasio, said in a statement Friday. “We won’t tolerate that, and the Mayor believes that behavior should be met with the toughest punishment available under the law. The Mayor has also been clear that there were parts of the video that gave him real concern.”