The President of University of Limerick has said students not adhering to public health advice will be dealt with under the university's code of conduct.
Professor Kerstin Mey said UL is carrying out investigations where she said there was "clear evidence that there was a breach of the public health measures".
Prof Mey was speaking on RTÉ's News at One amid a number of outbreaks of Covid-19 among third-level students in Galway and Limerick, according to the Health Protection Surveillance Centre.
Clusters of between two and 40 have been detected during testing of students with an average of two to three households mixing.
Overall, 120 students have tested positive at UL, which Professor Mey moved to clarify "did not come into being through activities on campus, in terms of learning and teaching".
"We have a student code of conduct under which we can deal with students who are not adhering to public health measures," said Prof Mey.
"If they bring the university into disrepute we have investigated students and we are investigating students where we had clear evidence that there was a breach of the public health measures."
Prof Mey said the university has been working with student unions to try to raise awareness to support compliance with public health measures, but she said the university has not been able to continue onsite patrols under Level 5 restrictions, like it had undertaken in September.
She explained that around 500 students have availed of on-campus testing since it became available last week.
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Earlier, the Students' Union President at UL urged students returning to campus or shared accommodation to act safely, but said there has been incidences where a positive case of Covid-19 has spread rapidly in a household where self-isolation can be difficult.
Speaking on RTÉ's Morning Ireland, Cian Ó Caoinleáin said that many students returning to the city and college campus after Christmas were seeking better broadband and adequate study space that was lacking in their homeplace.
Mr Ó Caoinleáin said that younger students who live on campus returned to study onsite. Many found this lockdown very tough and were longing for the sense of freedom and to meet friends away from home, he explained.
However, he said a minority may have a lackadaisical attitude and were "ruining it for others" by not adhering to Government guidelines.
Meanwhile, President of NUI Galway Students' Union Pádraic Toomey said a lot of the students in the younger years would have returned to campus last weekend and many came in because the broadband is better in Galway than in more rural areas.
Also speaking on Morning Ireland, he said he believes the increase in Covid cases is not due to parties or socialising but is related to people moving back into mixed households.
Galway has an unusual title of the highest number of students, not from its catchment area, he said, which means students from all over the country coming to one place which is "always going to cause a little bit of trouble".
Mr Toomey said students do not want to catch the virus at the campus and want to feel safe when they return home to visit their families.
There is a testing centre on campus and students were able to get a test over the weekend to "get a grasp" on the situation, he added.
He urged students to batten down, stay inside, stay with their housemates and stay safe.