Detroit’s black police chief is under fire over his department’s handling of a neo-Nazi group’s protest of a LGBTQ Pride festival, and comments he made in the days after the event that equated counter-protesters with the neo-Nazis.

Chief James Craig told reporters at a press conference this week that “both sides were wrong” and repeated a similar claim to the Detroit city council, which outraged some members of the public and counter-protesters, many of whom are black.

Craig told reporters: “Both groups were taunting our officers with racial epithets” and counter-protesters were “masked-up and referring to our African American officers inappropriately”.

However, Meeko Williams, a black counter-protester, said Craig’s claims were untrue.

“We don’t tolerate racism, and we told [officers]: ‘You’re black. The Nazis will kill you, too. They don’t have any respect for African American police officers,’” Williams said. “They were threatening to shoot cops, calling [officers] monkeys and N-words, and my comrades were trying to get officers to break rank and turn them back against the Nazis.”

Craig’s comments appeared to echo Donald Trump’s remarks after the 2017 Charlottesville Unite the Right rally in which a far-right protester was convicted of murdering a counter-protester and injuring eight others by driving a car into a crowd. Trump said there were “very fine people” on both sides.

The Motor City Pride festival took place in downtown Detroit’s Hart Plaza last weekend. About 15 members of the neo-Nazi National Socialist Movement marched at the event. They openly carried three rifles, two handguns and other weapons, according to police.

The group tore up a rainbow Pride flag and shouted racist and homophobic abuse. The neo-Nazis also made chimpanzee noises toward black people and police officers, according to multiple witnesses, while photos show one member of the group appearing to urinate on an Israeli flag.

Members of the National Socialist Movement tear apart a Pride flag at in Detroit, Michigan, on 8 June. Photograph: Jim Urquhart/Reuters

About 15 Detroit police officers formed a human barrier around the neo-Nazis and escorted them as they marched. Video shows police, some of whom were wearing rainbow Pride pins, pushing counter-protesters. In one video of the incident, a counter-protester appears to be asking officers: “How come they get protected, but we’re not?”

The police strategy prompted accusations that they were protecting neo-Nazis instead of those attending the event and the public. When asked by reporters on Monday about the department’s strategy, Craig replied: “Everyone has a right to freedom of speech, but you don’t have a right to engage in unlawful conduct.”

He later added: “We kept the distance between both groups, and there was no violence … It could have been a bad situation had it erupted into violence. It did not.”

Craig also told the Detroit city council at its regular Tuesday meeting that officers surrounded the marching neo-Nazis and created a “buffer” to avoid a confrontation between the two sides, adding: “Our strategy worked.”

However, bodycam footage that appears to have come from one of the neo-Nazis shows one of them assaulting a woman. The woman, Jessica Prozinski, posted the video to social media. It shows the neo-Nazi knocking her to the ground as she walks in front of them. She said police witnessed the encounter but took no action.

“They saw what happened, but they weren’t protecting us. They did nothing,” Prozinski said. “It was disgraceful. They provided Nazis with an armed escort up to the gate of Pride where people were in line. I have bruises on my arms, but they’re from the police.”

Police also received criticism for not informing the public that the neo-Nazis would be protesting at the festival. Craig said his department was aware of the plans a week ahead of time, but didn’t inform the public or city council in an effort to prevent large clashes.

“They didn’t just want to do what they did in Charlottesville; they wanted an enhanced version of Charlottesville,” Craig told city council.

Though there’s currently no evidence that Detroit police worked with the neo-Nazis, police in California, Oregon and other states have coordinated or maintained friendly relationships with far-right groups ahead of similar protests. Police at Michigan State University in early 2018 took a much more passive approach when hundreds of protesters blocked neo-Nazis from entering a Richard Spencer event. That broke out in violence that resulted in injured neo-Nazis fleeing campus.

Williams said Detroit police should have been “escorting the Nazis out of downtown, up I-75 … and out of the city.

“The image of black police officers protecting white Nazis in a majority African American city is a bad image,” he said. “This is horrible for Detroit.”

A police spokesperson said Craig was not immediately available for comment.