Gerard Craughwell has appealed to Government members to vote for him in the Seanad by-election, stressing he is independent.
He also said he is seeking legal advice on the possibility that John McNulty could be elected to the Seanad.
There was widespread criticism over the selection of Mr McNulty as the Fine Gael candidate in the by-election and his appointment to the board of IMMA.
John McNulty resigned from the IMMA board and asked for his name to be withdrawn from the by-election.
This evening John Deasy urged Fine Gael members to vote for John McNulty, despite Mr McNulty having asked members of the Oireachtas not to vote for him.
Mr Deasy described the situation as ridiculous and said it needs to be brought to an end.
Minister for the Environment Alan Kelly has also said he will vote for Mr McNulty in the Seanad by-election by default "as he has no option".
Mr Kelly said he has not voted yet because his ballot paper is at home in Tipperary.
He said voting for the two Opposition candidates is not an option.
He said: "To be honest with you, my position on it is very simple. I have no intention in voting for a Sinn Féin candidate, I have no intention of voting for a candidate supported by Fianna Fáil, so in that scenario, I believe in voting - I have no option, by default, but to vote for what was the Government candidate.
"It was was always my intention, and I'm not going to change it."
Earlier, Minister for Arts Heather Humphreys said she was not at liberty to say who mentioned Mr McNulty to her as a potential member of the board of the Irish Museum of Modern Art, because she said that was a Fine Gael matter.
Questioned by journalists in Dublin this morning, Ms Humphreys confirmed that Mr McNulty's name had been mentioned to her.
She went on to say that she takes full responsibility for his appointment.
"I'm not at liberty to say who mentioned his name to me, because that's a Fine Gael matter. I got his CV, I looked at it, I assessed it, and I take full responsibility for appointing him to the board of IMMA," Ms Humphreys said.
Questioned as to what she had meant when she stated previously that valuable lessons "had been learned", the minister declined to elaborate.
The minister was also asked why she had decided to appoint additional members to the board of IMMA when there were no vacancies.
She said she felt she could improve the representation of the regions by appointing two more people, based on their merit.
The minister said 15 people can serve on the board and there had been nine people on it.
Ms Humphreys said people who wanted to serve as volunteers on boards should be lauded and appreciated.
Minister for Jobs Richard Bruton this morning said errors were made in how the McNulty affair was handled but he did not say who made those errors.
The minister also said he fully supports Taoiseach Enda Kenny and his leadership has not been damaged.
Mr Bruton described last night's parliamentary meeting as constructive.
Mr Kenny has reiterated that measures he is putting in place will address any errors that happened over the past fortnight regarding the McNulty affair.
Speaking in Waterford at a job announcement, the Taoiseach said some of those errors were internal to the party.
He said they have now been addressed and a system will be put in place to look at the broader subject of appointments to State bodies.
Mr Kenny said: "We set out ... a Government decision with a memo setting out the criteria that will apply for all public appointments to State boards from now on.
"That means that from 1 November every minister, each minister will set out in respect of the boards under their responsibility the conditions, the criteria, the skill set, the expertise that will be required.
"The public can then apply on stateboard.ie. They will know the locations where opportunities arise to give public service and they will know the conditions and the criteria that are required."
During Leaders' Questions in the Dáil, Fianna Fáil's Robert Troy said that the Government could not move on from the McNulty affair until basic questions are answered.
He said it was ludicrous of Ms Humphreys to refuse to speak in public on the issue while she can speak to the Fine Gael parliamentary party.
Sinn Féin's Mary Lou McDonald said that with each passing day the details of the McNulty debacle become less clear and she accused the Taoiseach of waffling on the issue.
Tánaiste and Labour leader Joan Burton said the Taoiseach had explained details of events on several occasions, both in the Dáil and outside.
Independent TD Mick Wallace, who was speaking on behalf of the Technical Group, said the Taoiseach's "jobs for the boys" debacle has only added to people's sense of frustration with the Government.