Wolverhampton council leader Ian Brookfield said dozens of people escaped serious injured following the incident last week.
About 50 people were involved in the brawl which saw four police officers injured, three vehicles damaged and items of uniform stolen from one of the police vehicles.
The incident also resulted in police being forced to use riot shields as they were pelted by missiles thrown in their direction.
It took place on Ruskin Road just before 5pm on Wednesday, with locals saying the scenes were the result of children 'running around with knives'.
Councillor Stephen Simkins, deputy leader of Wolverhampton Council, has now called for more police officers to ensure people can be kept safe.
Police are said to be reviewing footage of the incident to work out what happened, though the force is yet to confirm why it was initially called to the scene.
Councillor Brookfield said: "The sort of disgraceful scenes we saw in Fallings Park this week are wholly unacceptable – and it is incredibly lucky that more people weren't seriously injured.
"As a responsible local authority, we remain committed to working with the police and other organisations to tackle the scourge of violence and knife crime in order to make our streets safer.
"We have a range of initiatives underway to help achieve this, working with children, young people, families and communities.
"Last week's incident is subject to an ongoing police investigation, and I would encourage anyone with information that might help apprehend the culprits to contact police on 101 as soon as possible."
One resident said police had taped off the street to deal with the situation, which saw a child brandishing a weapon running in the street.
However, the resident added that the brawl escalated as locals demanded something was done about the situation.
Councillor Simkins, deputy leader of Wolverhampton Council, said: "It is no surprise that the lack of police presence across the country and in Wolverhampton gives people the feeling that there are no repercussions.
"Not having that presence and reassurance for residents allows people to tempt fate, for want of a better phrase.
"We will be working with the police and reassuring residents that the authority will do everything we can to mitigate crime that is taking place.
"I think we should have more police numbers and sufficient numbers for their safety as well as the public.
"If there is anything we can do as an authority we will do it, violent crime needs to be addressed head-on."
Police are looking for any information on incident, a spokesperson said: "We're keen to hear from anyone with information as we establish exactly who was involved.
"You can contact us directly via our website and quote log 3152 of 20/7/22.
"Alternatively, you can speak to Crimestoppers anonymously on 0800 555111. Tell them what you know, not who you are."