Minister for Health Stephen Donnelly says the games themselves are not the issue regarding limiting attendances to 200 at sports events.
The Government again delayed Ireland going to Phase 4 of the roadmap for the easing of Covid-19 restrictions on Tuesday, meaning crowds remain limited to 200 at events, while pubs that don't sell food will remain closed.
But Mr Donnelly stated on Wednesday that the concerns around games is what happens before and after them rather than during them.
He told RTÉ Radio 1's Morning Ireland: "NPHET's [the National Public Health Emergency Team] position on this is, they actually don't see much of an issue during the game.
"The GAA and various other sporting organisations have some large stadiums. Their view is, of course you can have more than 200 people at an outdoor event properly spaced. Their concern is what happens before the match and after the match.
"For example, some of the clusters we're looking at at the moment, the belief is that some of the transmission may have been in the cars, on the way to work on the way from work.
"The public health experts, their view is, the match itself is not a problem. But people congregate beforehand, people share cars, people congregate afterwards and that really is their concern."
He added: "I think if the number of cases was consistently at less than 20 a day, which we had seen for some time, my sense is the public health officials would say, 'we're in a stable place, that's a low level of community transmission'," he added.
"Their concern is things are very, very finely balanced and they believe that it might take very little to tip this over into a situation where it begins to go out of control."
GAA president John Horan urged GAA fans to remain patient after Tuesday's announcement.
He said: "We don't want our members becoming too despondent or disheartened.
"What's important is that we have the games back and we keep them back and we continue to be vigilant and show leadership.
"This isn't going as fast as we want but we're still moving in the right direction.
"We made a strong case to both the Government and NPHET around the use of our bigger stadia for crowds of up to 400 excluding the players.
"But, obviously, with the numbers turning in the last few days they felt they couldn't acede to our request and we have to respect that decision."
