The Cabinet today agreed to a review of procedures following a discussion over the controversial appointment of former attorney general Máire Whelan as a judge to the Court of Appeal last week.
Ms Whelan was appointed yesterday, amid criticism over the process of her nomination and calls from Fianna Fáil for her to stand aside.
The review will be carried out by Martin Fraser, Secretary General at the Department of the Taoiseach.
A Fianna Fáil motion on the controversy in the Dáil this evening has been withdrawn after they failed to agree to question time during the motion, as opposed to speeches.
It is understood they will seek to have time for the issue to be discussed tomorrow.
The Social Democrats this afternoon accused Taoiseach Leo Varadkar of putting unseemly pressure on the President to appoint Ms Whelan.
The party believes the appointment breached protocols around the separation of the Office of President from the Government.
Joint party leader Róisín Shortall said former minister for justice Frances Fitzgerald still has questions to answer about how the appointment was handled.
Yesterday, Mr Varadkar said that the appointment was appropriate and lawful.
Most did not have full facts over appointment - McGrath
Minister of State with Responsibility for Disabilities Finian McGrath this morning said "the vast majority of people did not have the full facts" when the Cabinet approved Ms Whelan’s appointment to the Court of Appeal.
Speaking on his way into the Cabinet meeting, he said the Independent Alliance did make its views known on the issue but he could not say more because of Cabinet confidentiality.
Mr McGrath said it was only the Independent Alliance and Minister for Transport Shane Ross who had been pushing for reform on judicial appointments.
Minister for Communications Denis Naughten said legislation on judicial appointments must be prioritised as it is important that there is a transparent system.
The independent minister said that he has secured a commitment from the Taoiseach that the practice of "underarm memos" where issues are brought to Government without being flagged first will not be continued.
He said there were a number last week and the previous week and he raised it with the Taoiseach's office and with Mr Varadkar.
Minister for Health Simon Harris has said that he is very satisfied with the process which led to the appointment of Ms Whelan to the Court of Appeal.
Speaking this morning, Mr Harris said that after a week of talking about it, it is time to move on and address the major issues affecting the Government.
Minister for Agriculture, Food and Marine Michael Creed has also said he is "absolutely" happy with how Ms Whelan's appointment was handled.
Speaking in Washington DC, Mr Creed said that in the discussion that has surrounded how the appointment was made nobody was "suggesting that she isn't up to the job" and nobody was suggesting "that the Government acted outside of the law".
He said Ms Whelan had an "excellent legal brain" and is "highly qualified" for the job.
He said the law currently stated that "it's the Government's prerogative to appoint judges and that's what happened".
He said there had been a "collective Cabinet decision" made last week.