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 Agricultural Minister Dara Calleary and EU Commissioner Phil Hogan who both resigned.
Mr Hayes says he hopes people will recognise that his apology is sincere.
"I said it at the time and I will repeat it: I very much regret it and I apologise unreservedly for it.
"I think what is 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".
Speaking on The Hard Shoulder on Newstalk this evening, Mr Hayes said he hoped that people would accept his sincere apology.
He said that he shouldn't have allowed himself to "get into that position".
When 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."