Police didn't immediately make clear if those in custody were affiliated with the Proud Boys or the group of protesters.
At one point in the surveillance video, a group of people is seen throwing people they confronted to the ground before punching and kicking them. Police said there were no serious injuries in the fights and that they were reviewing footage to determine if other crimes were committed.
City Councilman Rory Lancman, also a Democrat, said video shows police officers were at the scene of an assault by Proud Boys members but did not arrest anyone from the group. The male-only Proud Boys describe themselves as "western chauvinists".
Proud Boys, a misogynistic and anti-Muslim fraternity known for acts of political violence, has been characterized as a hate group by the Southern Poverty Law Center.
The three arrested face assault charges and are awaiting arraignment Saturday in Manhattan criminal court. He urged the public to come forward with information that could help identify those involved. That video sparked outrage that police didn't arrest anyone at the time. The NYPD contested that and said 48 officers were on the scene Friday with the primary mission to keep the two sides apart, arguing the police presence was more than adequate.
Later on Monday afternoon, the NYPD's top uniformed officer, Chief of Department Terence Monahan, and its chief of detectives, Dermot Shea, held a news conference in which they explained in greater detail what had happened late last week, and what the department was trying to do about it now.More news: Hunter kills British cyclist in France, police speak of accident
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Shea said Monday that three more protesters were to be arrested for the brawl, too.
The Republican club was vandalized ahead of Friday's speech by McInnes, who is also a co-founder of Vice Media. Photos showed windows smashed in.
Republican leaders called on Democrats to denounce the vandalism. "I'm embarrassed these individuals were invited to speak", Molinaro said during a 90-minute appearance before the Daily News Editorial Board.
The note left at the club did not mention McInnes specifically, but accused Republicans of inviting "a hipster-fascist clown to dance for them, content to revel in their treachery against humanity".
Members of the City Council and the state Assembly went a step further, calling on State Republican Party Chairman Ed Cox to step down.