The Boston Police Patrolmen’s Union chief is calling for full prosecution of three dozen people arrested at the Straight Pride Parade Saturday, saying District Attorney Rachael Rollins and judges need to come down hard or risk more violence.

“They should all be prosecuted,” said Michael Leary, whose union represents Boston’s rank-and-file police officers. “We all just do our jobs and hope the courts do their jobs.”

The 36 people arrested at the controversial parade on Saturday will begin appearing in court Tuesday. Nine are accused of assaulting cops, injuring four officers. Those defendants and others were variously charged with assault and battery with a dangerous weapon, carrying a dangerous weapon, resisting arrest, and disorderly conduct.

The Herald witnessed protesters getting into altercations with police officers and one self-identified member of the hard-left group Antifa told the Herald that violence, while masked, is necessary to “shut up” the Straight Pride organizers. Antifa tweets claimed anti-parade protesters were most of those arrested.

Leary told the Herald, “We’re made up of laws, and people have to follow them. If you can do anything with impunity, that’s when things start to slide downhill and we end up in a bad place.”

Rollins’ office has said she’s “reviewing each arrest and will make informed decisions based on the facts of each and the policies of this office.” Rollins maintains a list of crimes that includes resisting arrest and disorderly conduct that she won’t prosecute as stand-alone crimes.

Cops said they used pepper spray after people threw so-called milkshakes at them — liquid concoctions that sometimes include chemicals — and that officers found handcuff keys and razor blades on some people they detained, according to published reports.

Some of the higher charges, including assault and battery of a police officer, aren’t on Rollins’ no-prosecute list, and her spokeswoman did say she won’t tolerate “violence or behavior that creates a risk for other participants, bystanders, or police.”

But Rollins’ office wouldn’t respond to questions on Monday about how tough a stance she intends to take in court — or whether she is concerned that leniency might encourage further violence.

Mayor Martin Walsh has said that he is concerned about allegations of “police misconduct,” and denounced the Straight Pride marchers.

Walsh on Monday morning said, “What I don’t want is a repeat of what happened in Charlottesville. That’s why we brought in so much security here, to make sure that people are safe. It’s the innocent bystanders that I’m afraid of, it’s people that might be coming to see what was going on and to oppose what this group was spouting, which I completely oppose.”

Leary said of his police union membership at Saturday’s parade: “You have people screaming at them all day long that they’re fascists and that they’re the bad guys. How would anybody like to have projectiles thrown at them all day?”

Leary added bottles full of an unidentified liquid were flying at the cops “frequently.”

Efforts to reach most of the arrested were unsuccessful.

Tiana Miles, 28, of Allston, who is due Friday in court on a charge of assault and battery with a dangerous weapon, told the Herald she was protesting the “bigots” when she claims someone in the parade yelled racial slurs at her. She said she splashed water at the man and was arrested. Roderick Webber, 45, of Holbrook, charged with disorderly conduct and resisting arrest, told the Herald he was just a “documentarian” shooting video. He said police charged at the crowd after someone apparently threw a bottle of urine at officers. He was caught up in the crush.

“It was nonsense — total shenanigans,” Webber said, claiming police indiscriminately maced people.