The Attorney General Paul Gallagher has briefed the Cabinet on the “serious constitutional issues” arising from the stand-off between Chief Justice Frank Clarke and Judge Seamus Woulfe.
Mr Gallagher outlined the serious constitutional issues that now arise and the respective responsibilities of each of the organs of the State as set out in the Constitution, including the roles of the Judiciary and the Oireachtas.
According to a statement, ministers who are also Members of the Oireachtas, are acutely aware of the sensitivity and seriousness of the issues and would avoid "inappropriate public comment".
“The Government agreed that it will continue to reflect on these issues,” the statement said.
The Government is under mounting pressure after Mr Woulfe rejected a suggestion that he should step down from the Supreme Court over the 'Golfgate' scandal.
The Finance Minister has described the controversy as a "very very serious matter".
Judge Woulfe has been told by Chief Justice Frank Clarke that he should resign but is refusing to do so.
Judge Clarke said he had come to the conclusion that on foot of Judge Woulfe's attendance at the ‘Golfgate’ event and later commentary around it, his departure from this office is now required.
The controversy was initially sparked when it emerged that more than 80 people, including Seamus Woulfe, had attended an Oireachtas golf society event in Clifden, just after the government tightened restrictions on gatherings.
Former Minister Shane Ross has said Seamus Woulfe should resign from the supreme court.
"It's utterly unprecedented that judges should be at war with each other in this very very public way and that's what's happening. So I think the Cabinet will be asked to do something about this," he said.
The former Minister for Transport said the judge should be held to the same standards as politicians and should resign.
"He shouldn't resign because Frank Clarke tells him to, because Frank Clarke basically wants to get rid of this problem.
"He should resign because he should be held to the same standard as politicians were.
"It's quite obvious that Supreme Court, which is under enormous amount of pressure and focus, and unwelcome focus at the moment, has handed this over to the Attorney General to brief the government.
"My guess is that the Cabinet will probably discuss it in some way, maybe not in a very broad way today," he told Newstalk Breakfast.
Sinn Féin's justice spokesperson Martin Kenny called on the Justice Minister and the Government to make "it clear" what way they will progress the matter.
Mr Kenny said: "Any of us that read the correspondence between the Chief Justice and Justice Woulfe, it's very clear the judiciary doesn't believe his position is tenable and that's really where all of this is coming from.
"We have to be careful with how we proceed here but at the same time we have to be firm, there has to be accountability."
He also hit out at the lack of progress on the Judicial Council Act which he said means that "we have a huge problem with the judiciary and how it is held to account".
However, Labour party TD Aodhán Ó Ríordáin said politicians must now "take a breath" and wait for advice from the Attorney General.
"We are in unchartered waters, this has not happened before, but we have to be careful what we say now there could be another case in five or ten years time, we don't know. So if you are serious about the Constitution, you are serious about your role in politics then what you say and the judgements you make obviously are going to have an impact."
He added: "The Labour party is quite clear on our position, we are determined to maintain the independence of the judiciary."