Minister of State for Sport Jack Chambers says he was 'shocked, appalled and horrified' by a photo of Gordon Elliott sitting on a dead horse.
Chambers says Elliott, who is under investigation by the Irish Horseracing Regulatory Board, "has to be held fully accountable for his actions".
The Minister told Morning Ireland on RTE Radio 1: "I was absolutely shocked, appalled and horrified by that photograph.
"It showed a complete and profound error of judgement and it was really disturbing from an animal welfare perspective.
"I think everyone across the country and even internationally who saw that photo was shocked and I think he has to be held fully accountable for his actions.
"I know there is an investigation by the Irish Horseracing Regulatory Board but it is important from an Irish perspective that we have the highest welfare standards and someone myself who grew up with animals and I think anyone, whether they did or they didn't, was shocked by that and I think consequences are important. He needs to be held fully accountable."
When asked if Elliott should be banned from training horses, Chambers added: "I think everything should be on the table. I think Ireland has to set a high bar when it comes to animal standards.
"We're talking about a dead horse here and I found everything that has been said so far doesn't explain what everybody saw.
"I was really, really disturbed by it and I think there has to be full follow through and everything should be on the table to make sure there's accountability and a high bar set for anyone who wants to work with animals in this country."
Elliott said his world is 'crumbling' around him as he apologised to the racing industry on Monday night.
The Meath trainer told the Racing Post: "It is indefensible. Whether alive or dead, the horse was entitled to dignity. A moment of madness that I am going to have to spend the rest of my life paying for and that my staff are suffering for.
"I will be punished, I fully understand that. But it absolutely breaks my heart to read and hear people say that I have no respect for my horses. That couldn't be further from the truth. My whole life has revolved around horses since I was a child. I know nothing else. Horses are all I have. I came from nothing and built a dream.
"When your world starts crumbling in front of you, it's a scary place to be. I just hope people can understand how truly sorry I am and find some way to forgive me for what I have done."
It came after British Horseracing Authority banned Elliott from having runners in the UK while the IHRB investigation is ongoing.
