Dr Cillian De Gascun, chair of the National Public Health Emergency Team (NPHET) Expert Advisory Group, said there is currently no "specific evidence" that Covid-19 was "particularly associated" with people who travelled to and from these events.
He said: "At the moment we don’t have specific evidence that the virus would have been particular associated with those groups of individuals.
"We are an island nation with significant transport links to other European countries on a daily basis. I don’t think we have evidence to support the assertion that they would have been points of introduction for the virus."
Professor Philip Nolan, who chairs the modelling advisory group on Covid-19, says if a second wave comes, there will be a more targeted approach.
It comes after more than 1,000 scientists and researchers called for the Government to suppress coronavirus rather than learning to live with the virus under a long-term mitigation strategy.
Professor Nolan said: "The second wave will be different from the management of the first wave. The wave is likely to be different and we know that a lot more about how to manage this virus than we did the last time.
Professor Philip Nolan, head of the Covid-19 modelling group
"So I imagine that there could be more targeted measures introduced to control the future outbreaks before the sort of blanket measures that we’ve seen in this context.
"It would be arrogant of me to predict where we will be with the virus by the end of the year. There is lots we don’t know. We need to plan as if a second wave is possible and try to have all of the contingency plans in place for that scenario if the virus comes back in the future."
When asked if society will return to full normality by the end of the year, he said: "I think our behaviours will be modified for some time to come."
Dr De Gascun has said the current Covid-19 testing system is working "incredibly well", but said a long-term solution is required.
"He said: Testing and tracing is important going forward but it must be in conjunction with hand hygiene and good respiratory etiquette. Testing is not a control measure in and of itself.
"The current testing scheme was set up in the context of a pandemic and I understand the HSE is working on a more sustainable longer term solution for the coming winter season.
"What we have done so far has worked well, but I believe given the way it has been established with the number of volunteers and staff seconded from other positions – a longer term solution is required."
Meanwhile, some 9,000 small and medium-sized enterprises (SMEs) could close for good following the Covid-19 crisis, the Covid-19 committee also heard.
Neil McDonnell, the chief executive of Isme, (the Irish SME Association), said that small business needs better support from the Government.
"We surveyed people on a sentiment basis around mortality and if anything close to the 6% that say they are done within a month, if that was to happen, you could be looking up to 9,000 SMEs," Mr McDonnelll added.
Mr McDonnell also criticised the Government’s business supports, including its restart grants for firms.
"What has gone into the sector by way of assistance is a drop in the ocean by contrast with what is coming out of the sector in tax," he added.
The coronavirus death toll in the country rose to 1,683 on Monday after a further four deaths were announced.
There were only nine new confirmed cases of the virus, the lowest daily tally since the early days of the outbreak in March.