Dáil will be recalled on Wednesday to debate the proposed challenge
Finance Minister Michael Noonan has branded an EU Commission ruling on Apple tax in Ireland as "bizarre and outrageous".
His comments come after Cabinet members unanimously agreed to appeal the ruling.
The comission is ordering Ireland to recoup up to €13bn in back taxes from the tech firm.
The EU body concluded this week after a three-year investigation that Ireland had granted illegal state aid to Apple, allowing it to pay just 0.005% tax in 2014.
The terms of the appeal will be drafted by Attorney-General Máire Whelan.
The Dáil is set to be recalled on Wednesday for a debate and vote on the issue, while the minority government has also promised a review of the tax paid by multinationals.
But Minister Noonan says that will exclude any look at our 12.5% corporation tax rate, which he claims is under attack.
Independent TD Katherine Zappone, who supports an appeal, says there will be a number of measures to ensure tax justice.
Junior Minister John Halligan insists that that the Government does not need to be destabilised with the budget and Brexit coming.
The Waterford TD says he will vote in favour of the motion in the Dáil next week.
Sinn Féin says the decision by Cabinet to appeal is wrong.
The party is also demanding that the full ruling be published before the Dáil debate.
Deputy leader Mary Lou McDonald claims governments did facilitate tax avoidance.
Independent MEP Marian Harkin is urging the Government to seek clarification from the European Court of Justice rather than mounting an appeal.
'A return to old politics'
The Social Democrats believe the appeal is the wrong course of action.
TD Róisín Shortall says: "We believe that Ireland should not appeal this decision and thereby further damage our international reputation.
"We should use unpaid taxation to improve our public services and national infrastructure and to reframe our industrial policy to make us more attractive as a place to do business internationally.
"That means improving infrastructure, broadband, public transport, housing stock and more.
"The European Commission finding does not seek to undermine our sovereignty or to set our taxation rates but rather finds an unfair advantage was given, as a state aid, to Apple."
She continues: "At the very least the Government should have presented the Dáil with expert views on the consequences of action before deciding to call for an appeal.
"The Government’s proposal to appeal the ruling sees a return to 'old politics' - so toxic in the 'old Ireland' - the same kind of politics which got us into this mess in the first place."
The Social Democrats say they will table an amendment to the Government's motion in the Dáil on Wednesday.