Councillor Peter Scott made the plea after reports of fighting, chucking glasses and walking in the road along High Street last Friday and Saturday.
Residents, on social media, claimed students from Harper Adams University were responsible for the disruptive behaviour.
It has since sparked unrest and resentment from older residents in the town with some staying at home due to the incident last week.
Police chiefs said they had not received any reports over the issue, but a spokeswoman for the university confirmed they had been alerted to an incident.
Councillor Scott called for unity and urged people to report the incidents immediately, to stop any spread of "resentment".
He said: "Something did take place, however, there were bits of broken glass on the street and I believe some people had been urinating into some of the flower pots.
"Some are saying students are responsible but I don't know – students don't go around with the word 'student' tattooed on their forehead.
"We must report it as it happens else it's just hearsay and it breeds resentment against students in this situation. If people comment on Facebook nothing will change.
"The first thing is, of course, we must deal with this anti-social behaviour wherever it pops up – but we don't know if it was students, not in this case.
"There's a lot of assumptions aimed against students but I think people should speak with the university directly because they can tell people what's happening.
"And, in my experience, once things have been reported to the university they can then deal with it properly. But let's not turn this into an 'us versus students' argument.
"It's young people who have had a few drinks – too many in fact – and they're letting off steam.
"We must be wary of blaming any particular group of people and, most importantly, if you see it report it to the police."
Councillor Scott said he would urge people to call police on 101 and contact the university, ensuring there was a proper report of the incident.
"The big problem with anti-social behaviour is people must phone 101 otherwise, strictly speaking, in the eyes of the law, it didn't happen," he added.
West Mercia Police said it was aware of concerns raised by residents on social media about the disorder – but said it had not received any reports of that nature.
Mike Phillips, Safer Neighbourhood Inspector for the area, said: "
We would always encourage people to report any concerns they have to us and be clear around the nature of the report and locations, it is only if we know about it that we can do something about it.
"I would like to reiterate that we are continuing to work with all establishments in Newport to ensure everyone is adhering to the Covid regulations and everyone is playing their part to keep people safe."
A spokeswoman for Harper Adams University said: "As always, we encourage anyone who witnesses inappropriate behaviour that might involve our students to contact with information to help us identify the individuals involved.
"Where a resident believes a crime has committed, we also recommend contacting the police on 101.
"We work closely with the local policing team, Pubwatch and other agencies to manage issues in the community.
"We were alerted to an incident on Friday night and have followed up with the people who contacted us."
The student services team can be contacted on email@example.com