"We want companies like Apple in Ireland... But this doesn't mean one should turn a blind eye to tax evasion or avoidance," Sinn Fein leader Gerry Adams said in parliament, which was recalled early to debate an issue that has divided the country.
"Tax is not just for the small man, it is for all," he said, Sinn Fein said on its Twitter account.
The European Commission last week ordered Apple to pay a record USD 15 billion in back taxes in Ireland, a move the US warned could damage hugely important transatlantic economic ties.
Ireland's two main parties, Prime Minister Enda Kenny's Fine Gael and Fianna Fail, which supports the minority government, are expected to back the appeal.
But Sinn Fein, the main opposition party which gained support in elections earlier this year on an anti-austerity platform, is set to oppose.
Sinn Fein finance spokesman Pearse Doherty said Apple had operated "a sort of untaxed Bermuda Triangle" in Ireland following opinion polls that have shown majorities in favour of Apple paying the back taxes.
"The government's position throughout this process has been that the full amount of tax was paid in this case and no State aid was provided," he said.
"Ireland did not give favourable tax treatment to Apple: Ireland does not do deals with taxpayers."
Prime Minister Enda Kenny said the ruling had done "great damage" to Ireland's international reputation.
"The picture of Ireland painted by the Commission in this decision as a country prepared to play fast and loose with the law to gain unfair advantage could not be more damaging or further from the truth," he said.
The European Commission said Apple paid an effective corporate tax rate of just 0.005 per cent on its European profits in 2014 - equivalent to just 50 euros for every million.
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