Brian Hayes says his attendance at the Oireachtas Golf Society dinner in August was "a big error of judgement".
The CEO of the Banking and Payments Federation of Ireland was at the controversial event in Clifden.
It was also attended by Supreme Court Judge Seamus Woulfe, former agricultural minister Dara Calleary and Phil Hogan, who later resigned as the EU Trade Commissioner.
Brian Hayes says he hopes people will recognise that his apology is sincere.
He told The Hard Shoulder: "Absolutely, I said it at the time and I repeat it I very much regret it and I apologise unreservedly for it".
"I think what's important is that people are proportionate about this and I hope people will recognise when people make mistakes, and they admit honestly that they made a mistake, that they can obtain an apology from people and more importantly that there's some understanding of that.
"That's something I've always said".
Asked if there was a disproportionate response to the event, he said: "It's really a matter for everyone to respond in their own way - and I think when people give an apology which is sincere and genuine, I would hope that would be accepted".
"I shouldn't have allowed myself to get into that position, Kieran, and I said that at the time and I publicly apologised and I'd do it again today.
"I wish it hadn't of happened and I apologise unreservedly for it.
Asked if he thought he was breaking the rules on the night, he said: "Yeah and I said that at the time... I wish I hadn't had gone into the room.
"And I fully accept that that was a big error of judgement on my part".