New York City can go ahead with an agreement to overhaul how the Police Department handles demonstrations, a federal judge ruled on Wednesday, rejecting arguments from the police officers’ union that the changes would endanger officers and the public.

The judge, Colleen McMahon of U.S. District Court in Manhattan, said in her ruling that the union, the Police Benevolent Association, had failed to show that safety would be compromised by the agreement, which calls for a gradual response to demonstrations rather than an immediate show of force.

“There is simply no evidence, let alone substantial evidence, that the public interest would be disserved if the settlement were approved,” she said.

If anything, Judge McMahon said, the methods the union proposed — responding quickly to protests with escalated force — would most likely be “counterproductive.”

The judge’s decision arrived as the city was engulfed in a fresh round of protests. There have been hundreds since Hamas attacked Israel on Oct. 7, and on Wednesday the authorities were preparing for disruptions to President Biden’s visit to New York.

The police union responded angrily to the decision to let the settlement go ahead. “The next time a peaceful protest is hijacked by rioters, the next time our roads, bridges or subways are shut down by agitators, New Yorkers should remember that their city chose to encourage these disruptions by signing onto this misguided settlement,” said Patrick Hendry, president of the P.B.A., in a statement.

Judge McMahon had approved the agreement last September following more than a year and a half of negotiations between the city and the office of Letitia James, New York’s attorney general. Ms. James had sued the department in January 2021 after an investigation found widespread abuses during Black Lives Matter protests following the killing of George Floyd in Minneapolis in the summer of 2020.

But Judge McMahon canceled the approval at the request of the police union, which had asked for a chance to argue against the agreement in court. The union, which was not sued in the case but intervened in the lawsuit, said it had “veto power” over the settlement because of its “interest in officer safety.”

The union’s move had threatened to upend the agreement reached by the city, Ms. James’s office, two other police unions, the protesters who had sued the department and the Legal Aid Society and the New York Civil Liberties Union. The last two groups had also filed lawsuits against the department after more than 2,000 demonstrators were arrested during the 2020 protests, most while demonstrating peacefully.

The images of violent confrontations stunned residents and municipal leaders, who called for dramatic changes to the way the department responds to peaceful demonstrations.

In September, Mayor Eric Adams and Edward Caban, the police commissioner, put out a news release supporting the agreement. Mr. Adams called it “the result of a collaborative process that seeks to build consensus, balance safety with justice, and protect protesters, bystanders and law enforcement personnel.”

But the P.B.A. objected to the deal’s four-stage system of de-escalation that would prevent officers from being deployed immediately.

In December, Mr. Adams retracted his support. “As soon as I read the settlement, I said, ‘This is a problem,’” Mr. Adams said during a news conference.

The deal that now will go ahead would end the tactic of boxing in protesters and then arresting them, a practice known as kettling that produced images of officers trapping protesters in tight spaces, then charging at them or beating at them with batons.

It also establishes a four-stage response to protests. First, for peaceful protests, officers from the community affairs unit would be dispatched to communicate directly with leaders and explain to them any action that might be taken.

The response will intensify in cases when officers believe illegal activity is about to occur or when the protest would block “critical infrastructure.” It would be further heightened if crimes have probably been committed.

The fourth stage, in which the police would move to end the protest, would be activated if protesters tried to get into or block the entrance of “sensitive locations” like a precinct, courthouse or hospital, or when crimes were so widespread that de-escalation or “targeted enforcement has not worked or cannot work.” Commanders on the scene would have to get approval from a supervisor to deploy officers.

The system is cumbersome and would prevent officers from responding nimbly, the union said in court papers. It ignores how quickly a protest “may degenerate rapidly and unpredictably into a violent encounter or riot,” union attorneys said in the brief, pointing to the Jan. 6, 2021, Capitol Hill riot.

During a hearing in federal court on Jan. 29, lawyers for the city and civil liberties groups said the union had misrepresented the plan.

The police will have discretion to deploy officers whenever they determine a protest has become dangerous, Corey Stoughton, a Legal Aid lawyer, told Judge McMahon.

The union made so many erroneous statements about the agreement, “it honestly often feels as if they didn’t read it” said Ms. Stoughton, who now works for Selendy Gay in Manhattan.