Violent confrontations at a pro-Palestinian rally in Bay Ridge, Brooklyn, on Saturday reflected what some local officials and protest organizers called an unexpectedly aggressive Police Department response, with officers flooding the neighborhood and using force against protesters.

At the rally, which drew hundreds of demonstrators, at least two officers wearing the white shirts of commanders were filmed punching three protesters who were prone in the middle of a crosswalk. One officer had pinned a man to the ground and repeatedly punched him in the ribs, a 50-second video clip shows. Another officer punched the left side of a man’s face as he held his head to the asphalt.

The police arrested around 40 people who were “unlawfully blocking roadways,” Kaz Daughtry, the department’s deputy commissioner of operations, said on social media on Sunday.

Mr. Daughtry shared drone footage of one person who climbed on a city bus, “putting himself and others in danger.” The Police Department, he wrote, “proudly protects everyone’s right to protest, but lawlessness will never be tolerated.”

Neither Mr. Daughtry nor the police commented on the use of force by officers. A spokeswoman for Mayor Eric Adams did not immediately respond to a request for comment about the police response. The Police Department’s patrol guide states that officers must use “only the reasonable force necessary to gain control or custody of a subject.”

Bay Ridge has a significant Arab American population and hosts demonstrations in mid-May every year to commemorate what Palestinians call the Nakba, or “catastrophe” — when hundreds of thousands of Palestinians fled or were forced from their homes during the war that led to Israel’s founding in 1948.

Andrew Gounardes, a state senator and a Democrat who represents the area, said local politicians had been in touch with the commanding officer of the 68th police precinct before the preplanned protest and said there had been no indication that there would be such a heavy police response. He called the videos he saw of the events “deeply concerning.”

“It certainly seems like the police came ready for a much more aggressive and a much more confrontational demonstration than perhaps they had gotten,” he added.

Justin Brannan, a Democrat who is the city councilman for the area, said the protest was smaller than last year’s but that officers had come from all over the city to police it. He said their approach appeared to be directed by 1 Police Plaza, the department headquarters in Manhattan.

“These were not our local cops. Clearly, there was a zero-tolerance edict sent down from 1PP, which escalated everything and made it worse,” Mr. Brannan said.

“I’m still waiting on information and details about the arrests that were made,” he added, “but from my vantage point, the response appeared pre-emptive, retaliatory and cumulatively aggressive.”

The Republican state assemblyman whose district includes parts of Bay Ridge, Alec Brook-Krasny, had a different perspective. He said an investigation would determine whether the officers’ actions were warranted, but he said some protesters were “breaking the law” by refusing to clear the street.

“I think that those bad apples are really hurting the ability of the other people to express their opinions,” Mr. Brook-Krasny said.

Some local residents supported the police and said they were tired of the protests’ disruptive impact. “Enough is enough,” said Peter Cheris, 52, a 40-year resident of Bay Ridge, who said he had viewed the videos of the protest. “If you’re going to break the law, you deserve it,” he said.

Donna Lieberman, the executive director of the New York Civil Liberties Union, singled out the presence of the Police Department’s Strategic Response Group, a unit that is sometimes deployed to protests and has been the subject of several lawsuits brought by the civil liberties union and other groups.

The police unit’s handling of the demonstration “was a violation of New Yorkers’ right to speak out and risks chilling political expression,” Ms. Lieberman said in a statement. “N.Y.C.L.U. protest monitors witnessed violent arrests, protester injuries, and even arrests of credentialed members of the press.”

She added: “The continual pattern of N.Y.P.D. aggression against pro-Palestine demonstrators raises important questions about the city’s disparate treatment of speakers based on their message.”

Abdullah Akl, an organizer with Within Our Lifetime, the pro-Palestinian group that organized the protests, said the response took organizers aback, particularly for a demonstration that occurs every year in Bay Ridge and is known to be frequented by families with children.

“It was really an unusual and unprecedented response,” Mr. Akl said.

He said he witnessed two men being pushed to the ground. One of them can be seen in a video with blood streaming down the side of his face. Nerdeen Kiswani, chair of Within Our Lifetime, said three protesters — including the two who can be seen being punched — were treated for their injuries at hospitals.

The Police Department has arrested hundreds of demonstrators since street protests began shortly after the Hamas attack on Israel on Oct. 7 and Israel’s subsequent invasion of Gaza. The protests have been largely peaceful, with few injuries or violent clashes.

In a turning point, on April 30 officers cleared Hamilton Hall at Columbia University, which had been occupied by protesters for 17 hours. Many officers showed restraint during the arrests, though a handful were filmed pushing and dragging students as they removed them from the building.

On Sunday, Ms. Lieberman said police response to the protests in Bay Ridge underscored the importance of implementing the terms of a $512,000 settlement the civil liberties union and the Legal Aid Society reached with the city this month. The settlement set new terms for how the Police Department manages protests, creating a tiered system that dictates how many officers can be sent to demonstrations and limits the use of the Strategic Response Group. It will take years to put into practice.

The settlement is one of several that stemmed from the George Floyd racial justice protests in 2020. Last year, the city agreed to pay $13.7 million to settle a class-action lawsuit that claimed unlawful police tactics had violated the rights of demonstrators in Manhattan and Brooklyn. In March, the city agreed to pay $21,500 to each of roughly 300 people who attended another Black Lives Matter protest in 2020 in the Bronx. Those people were penned in by the police, then charged at or beaten with batons, according to a legal settlement.

Andy Newman and Camille Baker contributed reporting.