Minister for Transport Shane Ross has called for a review of the circumstances surrounding the appointment of Máire Whelan to the Court of Appeal.
Mr Ross told The Irish Times he was not questioning Ms Whelan but the process of her appointment.
The Minister said the circumstances needed to be revealed, and he would be asking the Taoiseach at their next meeting on Tuesday to do so.
Mr Ross insisted there was no link with link between the reopening of Stepaside garda station and the appointment.
Mr Ross was the only Minister to question the process when it was discussed by Cabinet this week.
His intervention on Friday comes as Taoiseach Leo Varadkar sought to end the controversy by saying the Government followed proper procedures.
In his first comment on the affair, Mr Varadkar said Ms Whelan was highly qualified to serve as a judge in the court.
“The issue which is attracting comment however is solely a matter of procedure. I am satisfied that the correct procedures were followed,” Mr Varadkar said.
“Under Article 13.2 of the Constitution, the Government and only the Government can appoint judges. The Tánaiste recommended Maire Whelan to Cabinet as the stand-out person for the vacancy.”
Mr Varadkar also insisted he would fully respect the confidence-and-supply agreement between Fine Gael and Fianna Fáil.
However it did not require Fine Gael to inform Fianna Fail of public appointments.
The appointment was earlier described by Fianna Fáil as “a cynical political decision” and an example of “stroke politics”.
The party’s spokesman on Jobs, Enterprise and Innovation, Niall Collins, said the situation surrounding her appointment as a judge of the Court of Appeal “stinks to high heaven” and he called on Ms Whelan not to take up the appointment while so many questions remain unanswered.
Fianna Fáil supports the Fine Gael-led minority government under a “confidence and supply arrangement” whereby it supports the Government in Dáil votes or abstains.
The party’s justice spokesman, Jim O’Callaghan, told RTÉ’s Sean O’Rourke that under the terms of that agreement there was a “no surprises” clause and he believed “this was sprung on us all”.
Mr O’Callaghan said Independent Minister Shane Ross had ridden in on an a white horse but was now “party to a stroke”. Mr Ross has denied accusations that he agreed to the appointment in return for the re-opening of a Garda station in Stepaside in his constituency.
Mr O’Callaghan said the Government had been “deeply misleading” in its description of the appointment. “It is deeply troubling that three High Court judges didn’t have their candidacies considered.”
If Ms Whelan had gone through the usual procedures via the Judicial Appointments Advisory Board, Fianna Fáil would not have a problem with the nomination, he said.
Gerry Adams, leader of Sinn Féin, said the appointment of Ms Whelan did not follow the procedures set out by the Judicial Appointments Advisory Board.
Fianna Fáil's position "facilitated the election of this Government despite this being a breaking story at the time", he told RTÉ's Today with Sean O'Rourke show. "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.”
Minister for Communications Denis Naughten, and Independent TD, will raise the issue at next week’s Cabinet meeting. Members of the Independent Alliance are to meet today to discuss the appointment also. It is understood Mr Ross and Minister of State at the Department of Health Finian McGrath are extremely angered by the process and intend to raise it with the Taoiseach at next week’s Cabinet meeting.
The Irish Times understands Ms Whelan, who has been Attorney General for six years, did not leave the Cabinet room when her nomination to the appeal court was discussed on Tuesday this week.
Ms Whelan, who has not yet been formally appointed by the President, was a close ally of Taoiseach Enda Kenny, who publicly supported her during the aftermath of the Fennelly Commission, when she was strongly criticised, and her appointment was one of his last acts of office.
The Government spokesman said Ms Whelan was nominated in accordance with the Constitution and because she was “available and qualified”.
The controversy was a “test” for Leo Varadkar, Sinn Féin’s Mary Lou McDonald told Newstalk “Breakfast”. She said she was not casting aspersions at the ability of Máire Whelan, just at the manner in which the appointment was made.