Independent Senator David Norris has said he regrets any offence caused by the comments he made towards Fine Gael TD Regina Doherty in the Seanad yesterday.
During a debate on the abolition of the Seanad, Mr Norris complained of having to listen to the "the Regina Monologues" from a TD who "wasn't a wet week" in the Dáil.
Ms Doherty, who is Fine Gael's deputy director of elections for the Seanad referendum campaign, later confirmed she would be making a complaint.
Speaking in the Seanad this morning, Senator Norris said he wanted to withdraw the words that caused offence.
"I accept that my language was intemperate, had I been called for an explanation at the time I would have given one.
"I don't intend to go into a lengthy linguistic explanation and try to defend what I said, which I could if this was an academic discussion. I regret any offence, but I'd like to say this, that the thing I regret most is that this is going to be used in this dirty campaign as a diversion."
Minister for Expenditure and Public Reform Brendan Howlin said this morning that it was "regrettable debate should descend into personal animosity and personal commentary".
Elsewhere, Minister for Jobs, Enterprise and Innovation Richard Bruton has said "name-calling" must be avoided during the debate on the abolition of the Seanad.
Mr Bruton, who is his party's director of elections for the referendum, was speaking a day after he was accused of Nazi-style propaganda.
The minister had said the abolition of the upper house would save €20m.
Fianna Fáil Senator Mary White compared the €20m claim to Adolf Hitler's propaganda.
Senator Norris described a press release yesterday by Mr Bruton as a "malignant and mendacious piece of tripe".
Speaking on RTÉ's Morning Ireland, Mr Bruton said he was standing over his comments that the abolition of the upper house would save €20m.
He said that politics must make savings like any other family or business in Ireland. He said they must "do more with less".
Mr Bruton rejected claims the savings would be considerably lower than projected as some of the current spending on the Seanad was shared with the Dáil and would be incurred anyway.