Minister for Transport Shane Ross has called for a review of the decision by the Government to nominate the former attorney general Máire Whelan to the Court of Appeal.
Even though Mr Ross signed off on the nomination, he wants the decision reviewed.
Whether or not that could lead to the nomination being withdrawn was entirely up to other people, he said.
Mr Ross denied his support for the nomination last week was linked in any way to the reopening of Stepaside Garda Station, which is in Mr Ross’s constituency.
Fianna Fáil has said the nomination is a breach of its agreement to facilitate the minority coalition.
However, Taosieach Leo Varadkar has defended the Government's nomination of Ms Whelan.
Amid strong criticism from the Opposition about the manner in which Ms Whelan has been nominated to the court, Mr Varadkar said he is satisfied that correct procedure was followed and he was pleased that no one was questioning her competence or quality.
The Taoiseach said Ms Whelan had an outstanding legal mind and was highly qualified for her new role.
Mr Varadkar said he was satisfied correct procedures were followed and under the constitution only the Government can appoint judges.
He also said he was committed to the confidence and supply agreement with Fianna Fáil.
Earlier, Minister for Finance and Public Expenditure Paschal Donohoe said Ms Whelan's appointment of was made in a way that's "entirely consistent" with Ireland's constitution and the Government’s role in it.
Speaking on RTÉ’s News At One, Mr Donohoe said Ms Whelan is an outstanding candidate and the Government has the ability and right to make the appointment.
He added: "We have a supply and confidence agreement with Fianna Fáil that we honour, but such appointments are a matter for Government."
Fianna Fáil justice spokesperson Jim O'Callaghan said the appointment is mired in controversy and his party has a serious issue with it.
Speaking on RTÉ’s Today with Sean O'Rourke, Mr O'Callaghan said he does not want to personalise this issue but he thinks Ms Whelan should stand aside and her appointment should not proceed.
He said there is not a problem with her being appointed; the problem is she did not go through the judicial appointments advisory board.
"If an appointment is done in this fashion, if that is permitted, there is a shadow cast over the appointment process," he said.
Other Opposition leaders have also been critical, with Sinn Féin leader Gerry Adams describing the appointment as cronyism.
Labour Party leader Brendan Howlin said it seemed absolutely wrong for former taoiseach Enda Kenny to appoint Ms Whelan.
Mr O'Callaghan said it is only the Government that can appoint people to the bench, and that is something that should be maintained.
But he noted that there has been a law in place since 1995 which sets out how to identify the best candidates for judicial office, and said this was not applied in this circumstance.
He said if Ms Whelan went through the job process, Fianna Fáil would have no objection.
"It may be the case she is well qualified. But without going through the job process, it is mired in controversy."
He said Fianna Fáil leader Micheál Martin was the first person to raise the issue, and added: "It is now a significant political issue and if we can't find answers to the questions raised, then the nomination must be revoked."
He said Taoiseach and Fine Gael leader Leo Varadkar needs to know this is a threat to the Government.
"At the next meeting he needs to say this appointment should not have been made."
He said if the appointment goes ahead it will mean a breach of the confidence and supply agreement which sees Fianna Fáil support the minority Government.
"There is a provision within the confidence and supply agreement which said there should be no surprises. This is clearly a surprise that was sprung not just on Fianna Fáil but on the whole political system last Tuesday at a time when they thought they could sneak it through.
"It is my view that it would be a breach of agreement if this stands without the satisfactory explanations and assurances."
Speaking on the same programme, Mr Adams said the Government has questions to answers and has so far given no explanation.
"It did not follow procedures that was set out by the Judicial Appointments Advisory Board."
He said the big problem with the Fianna Fáil position is they "facilitated the election of this Government despite this being a breaking story at the time".
Mr Adams said: "We will be raising it in the Dáil. We have just had the coronation of a new Taoiseach. He talked about it being a Republic of Opportunity.
"I would like to see it about equality. And at the last meeting of Enda Kenny's cabinet, at which Leo Varadkar was present, they did this stroke."
Speaking on Newstalk, Mr Howlin said there has to be an objective set of criteria put in place that is open to any applicant to be tested on.
He said he is not questioning the capabilities of Ms Whelan, having worked with her in and out of government.
"I know her ability and I think she would meet any objective test for appointment to that position. That is the difficulty. On the face of what we know, there appears to have been no objective test and no opportunity for anyone else to apply for it.
"And that is just not right. We need to make sure that any position is done on the basis of not only merit but demonstrable merit."
He said Mr Varadkar needs to explain "in detail what happened, how this came about, were there other applicants, and were other applicants considered?"
He also criticised Independent Alliance minister Shane Ross for "having objective criteria for all appointments" but "seems to have sat on his hands in relation to these matters because his constituency issue has been addressed".
Mr Howlin was referring to the same Cabinet meeting, which reviewed a list of closed garda stations, and which approved the reopening of Stepaside Garda Station in Mr Ross' constituency.
Mr O'Callaghan said while he has no evidence of a side deal with Mr Ross getting Stepaside Garda Station reopened, he believes it.
