Labour will support a motion of no confidence in the Tánaiste, Leo Varadkar, which is being tabled by Sinn Féin.
Labour's Aodhan Ó Ríordáin said that while his party will support the motion, it believes there are bigger issues facing the country and priorities for discussion in Dáil Éireann next week
The Social Democrats have said they will decide on Monday whether to support the motion or not, before it is debated in the Dáil next Tuesday.
The Fine Gael leader apologised in the Dáil on Tuesday for "errors of judgement" after sharing an agreement reached with the Irish Medical Organisation to a rival group in April of last year.
The Tánaiste said he posted a copy of the document to the National Association of General Practitioners' president Dr Maitiú Ó Tuathail, on a confidential basis, to see if he could get the NAGP on side.
Sinn Féin leader Mary Lou McDonald has said she has no choice but to table the motion of no confidence in the Tánaiste, because the Taoiseach has "chosen not to act".
She said Mr Varadkar's account of events around the leaking of the document "do not tally with the facts."
"The facts are that Leo Varadkar, when Taoiseach, leaked a confidential document to one of his friends and that is not acceptable," she told RTÉ News.
"It is not merely bad practice, it is wrong. And it is not a way that anybody in that office can behave."
She said the party are moving this motion "because it is the right thing to do, we are moving this motion because the Taoiseach has chosen not to act and therefore the opposition has to act because he does have to face some level of sanction and some level of real accountability from the Oireachtas on behalf of the people."
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Ms McDonald said it is "not lost on people" that Mr Varadkar's behaviour is "the Fine Gael way" of politics.
"It is the politics of the nudge and the wink, the insider, the old boys' network and that is not acceptable. And the Taoiseach might be content to stand idly by but I certainly won't," she said.
Asked if it was an attempt to divert attention away from questions about the receipt of public money by some Sinn Féin representatives in the North, she said that particular issue was dealt with "speedily" and four people lost their positions as a result.
Taoiseach Micheál Martin has said he believes the Government will win the vote.
Speaking on RTÉ's Six One News, Mr Martin said the key issue facing our society is the pandemic and how it is affecting people, the economy and business and the government wants to focus on this.
He said that is what should command all of our attention and that the Sinn Féin motion, so early after a general election, is a destabilising move and he does not believe it is the appropriate or proportionate response.
Text of Sinn Féin no confidence motion in Leo Varadkar: pic.twitter.com/1cjn7s1g2g— Sandra Hurley (@sandra_hurley) November 6, 2020
Meanwhile a spokesperson for Mr Varadkar's spokesperson said "the Tánaiste dealt with all the issues in the Dáil this week.
"This motion clearly shows that Sinn Féin isn't interested in the truth.
"They're only interested in political mudslinging, attacking the Irish Government at a time of national crisis and diverting attention from the unanswered questions about their receipt of public money in the North."
Meanwhile, Minister for Tourism, Culture, Arts, Gaeltacht, Sport and Media Catherine Martin said that she has confidence in Mr Varadkar.
She said she had worked well with him up to now and continues to do so.
The Green Party Deputy Leader said the Tánaiste had acknowledged that what happened was inappropriate and had apologised for this.