A brawl outside a Republican club in Manhattan involving a far-right group and anti-fascist activists spurred calls over the weekend for an investigation into the violence and whether the police handled it properly. Some Democratic politicians, including Gov. Andrew M. Cuomo, also criticized the club for inviting the founder of the far-right group, the Proud Boys.

Mr. Cuomo said he has asked the Federal Bureau of Investigation to look into the violence that accompanied Friday’s appearance at the Metropolitan Republican Club by Gavin McInnes, a right-wing provocateur. He also assigned a State Police hate crimes unit to assist with the New York Police Department’s investigation of the fighting, which he linked to President Trump.

But state Republican Party leaders accused Democrats of trying to exploit the violence for political gain.

“We’re the victims here,” Deborah Coughlin, president of the Metropolitan Republican Club, said on Sunday, striking an incredulous tone after Mr. Cuomo’s remarks. The group’s building on 83rd Street on the Upper East Side had been targeted hours ahead of Mr. McInnes’s appearance by vandals who left a note that declared the attack “merely a beginning.”