Anthony Daly has aired his deep frustration with counties who have defied GAA instructions and continued to hold group training sessions this month.
Last Tuesday, with Covid-19 cases escalating and the conutry returning to Level 5, the GAA instructed counties that collective training was forbidden until February and warned that breaches would be dealt with under Rule 7.2 (e).
If found guilty, a team could face a minimum eight-week suspension, with fines, disqualification or even expulsion also possible.
However, there have still been reported cases of counties gathering for group sessions.
In an interview with the Irish Times, former GAA president Seán Kelly went as far as suggesting teams that break the training ban should be banned from the Allianz Leagues.
Speaking to RTÉ's Saturday Sport, Daly said: "I was mad, literally mad when I read some of the stories from various counties; managers telling us they were team building under medical supervision and not training, this kind of thing.
"For me, we look at the country, we look at our neighbours across the water [in England], I lost my first cousin yesterday in London, a very fit 72-year-old man... it's a no-go now. We just have to hunker down and get the thing in control. For people to be breaking that for inter-county or whatever, that's a no-go for me.
"Everybody has the methods now - be it through Zoom or whatever they use - everybody has an idea of how to get their programmes out.
"There's no excuses anymore. I just think a severe punishment has to be meted out, whatever it is, whether it's being thrown out of the league, maybe that's not severe enough, I don't know.
"It has to be coming from Croke Park, right from the top, to say, 'no, this is not being tolerated, no excuses are allowed here'.
Oisin McConville said mixed messages with regards to the regulations haven't helped, adding: "We were told we'd come under the umbrella of elite sportspeople. Elite sports teams are able to train and play.
"If you're an elite sports person in December, the chances are you're an elite sports person in January.
"If Sean Kelly wants to ban all the teams that were training and throw them out of the league we could have two or three teams left in the league, from the anecdotal stories I'm hearing.
"We either are elite, or we're not elite. We need to cut the mixed messages with regards to that."