Police commanders moved on Monday to quell a controversy over the department’s handling of brawls outside a Republican club in Manhattan, saying they were seeking nine people affiliated with the Proud Boys, a far-right group, and three additional anti-fascist protesters on riot and attempted assault charges.

The police on Friday arrested three protesters after an appearance by Gavin McInnes, the founder of the Proud Boys, prompting an outcry that none of his supporters had been charged for the videotaped violence.

The police released a video on Monday of one of the skirmishes and said it showed the chaos that officers confronted from a different angle than the videos that have been circulating on social media.

The trouble started, the police officials said, after fans of Mr. McInnes filed out of the Metropolitan Republican Club on East 83d Street and headed down Park Avenue. A splinter group of masked protesters looped around Lexington Avenue to intercept them, the police said.