The Government has been accused of "circumventing the law" to appoint the former Attorney General, Máire Whelan, as a judge.
Sinn Féin's Mary Lou McDonald described Justice Minister Charlie Flanagan's speech as a long-winded way of telling the opposition to mind its own business.
Mr Flanagan said it would be unconstitutional for him to discuss how three High Court judges were overlooked for a new job, in favour of the former Attorney General.
He said Cabinet discussions around who to nominate for judicial roles are covered by Cabinet confidentiality.
Minister Flanagan said it would also be unfair to the other judges to talk about applications they did not make.
He said: "In fairness to any such member of the judiciary who may have expressed such interest, we're hardly going to lay out for political and public consumption the names and details of serving judges who have chosen to put themselves forward for more senior positions.
"Would we not be rightly castigated for doing such?"
Fianna Fáil also said the laws on judicial appointments, introduced by Fine Gael after a similar controversy, were "simply ignored".
However, it has emerged during a Dáil debate that the Fianna Fáil leader Micheál Martin rang Taoiseach Leo Varadkar on Sunday to complain about Ms Whelan's candidacy.
Ms McDonald said that is a sign that Mr Martin is trying to control matters he should not.
She said: "The conversation was not just a casual tete-a-tete between the leader of Fine Gael and the leader of Fianna Fáil.
"It was very directly an attempt by Micheál Martin to prevent an appointment to the bench by government."