The Government is pressing ahead with the appointment of former Attorney General Maire Whelan to the Court of Appeal.
Despite controversy surrounding the move, Ms Whelan's appointment will be formalised by the President tomorrow morning.
Fianna Fáil leader Micheál Martin warned that the Irish judicial system is at risk of being undermined by the appointment of Ms Whelan to the Court of Appeal.
Speaking last night, Mr Martin said: "This row has the potential to undermine the stature of the judiciary" and added that "Ms Whelan should consider her position".
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However, the Government continues to maintain that the decision at a Cabinet meeting last Tuesday to appoint Ms Whelan was entirely legal, and that she is eminently qualified for the position.
The new Minister for Housing has said he believes that correct procedures were followed when appointing the former Attorney General to the court.
Speaking on RTÉ's The Week In Politics, Eoghan Murphy said "nothing tells us that the correct procedures were not followed".
However, Fianna Fáil's Dara Calleary criticised the Government's selection of the former Attorney General to the court when he said three High Court judges had expressed an interest in the role.
Speaking on the same programme, he said that they need to look at the process of the appointment and why Ms Whelan was at the Cabinet table when the position was being discussed.
Independent Alliance Minister for Transport Shane Ross said he will bring his concerns over Ms Whelan's appointment before Cabinet on Tuesday.
The minister said the Independent Alliance was firm that the process for nominating and appointing judges needed to be changed.
He has no issue with Ms Whelan's qualifications, he said, but said the system needed to be reformed.