GAA president John Horan has called on the Government to give the association permission to allow outdoor gatherings of over 200 people.
Wednesday's decision to halt entry to Phase 4 of the Covid-19 roadmap means less than 200 people can attend outdoor events into mid-August, rather than the 500 the GAA had been preparing for from next week.
"The change in attendance guidelines has delivered a hammer blow to the organisation," Horan told RTÉ Radio 1's Morning Ireland.
"We put the return to the club game first to benefit our members and help out county boards survive for those clubs but our county boards were relying on an increase to 500 as a way of being able to cater for the demand on the ground from our supporters.
"They now have the extra burden of continuing to police 200 being in attendance.
"If you take those involved in the teams and stewarding out of it, you're probably looking at 120 supporters going to a game.
"If you work out the dimensions of a GAA pitch, that allows for social distancing of four metres between everybody attending the match.
"We have also encouraged everybody to wear face masks, so I think these figures are a bit severe on us as an organisation, and I openly call on the Taoiseach and Tánaiste to go back and review those figures for us as an organisation.
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"The risk factor outside is 1 in 19 in comparison to indoors.
"We have stadia throughout the country which can cater from anything from 6,000 to 50,000 people and to say that you can only have 120 supporters put in... I think the volunteers in our organisation acted totally responsibly in this pandemic and I don't think if we allowed them to increase the attendance from 200 to 500 that they would act irresponsibly."
Horan added that GAA members should "absolutely" continue to follow NPHET guidelines, but said he felt there was "room for a small expansion".
"If you look at the caution we have taken as an organisation: we extended the date on dressing rooms; I would still urge people to be cautious, wear the face masks," he said.
"All we are trying to do is get people to be active outside and there is a pent-up demand for people to go to these matches.
"I don't think by calling for an increase from 200 to 500 that I'm putting public health or anybody at risk.
"We have put a lot of education and protocols in place to protect those involved in our games and I think it is a safe call to say we could cater for 500 in our stadia.
Relating to the rise in younger people contracting Covid, Horan said those in the GAA "have got to make a clear decision. Either you party or you play sport.
"Sport and partying are not going to work at the moment because it's partying that has brought many of these challenges to our doors as regards to the virus.
A number of GAA clubs have suspended activity after members tested positive for Covid-19, which Horan said was not unexpected.
"GAA clubs are mingled into society and society has the pandemic out there so it was always going to come to the door of the clubs.
"But the one thing I would credit all our officers and people within our clubs with, they have complied with the guidelines we have given them.
"Clubs that had a case arising on the club or near the club have actually applied the guidelines, contacted public health, and most of those clubs have reopened immediately."
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Kerry football legend Pat Spillane backed Horan's call, citing an example from his own county.
"I agree with John Horan," he told the RTÉ GAA podcast.
"Will someone beat sense into someone and say there is no problem having 500 people in these GAA stadiums? It's not a health issue.
"How can you have the situation where you can have 800 people in a shopping centre but you can't have more than 200 people outside in the fresh air?
"Next Friday, the first round of the Kerry senior football championship is on. Templenoe play Dr Crokes in Fitzgerald Stadium, Killarney.
"It takes 45,000 people. At maximum, there will be 100 people dotted around the stadium. Holy God. With social distancing it could comfortably take 3,500/4,000.
"Let's ditch the one-size-fits-all approach. Let's look at it case by case. Have the GAA the stadia to fit 500 people socially distancing? Yes, they have.
Clare All-Ireland winner Anthony Daly conceded that the GAA might have sought to make a joint declaration with other sporting bodies rather than a solo appeal, but said the change had been "foisted on" the association at short notice.
"It's a joke that 500 people couldn't be at a standalone fixture with loads of room."