Update 8.50pm: Communications Minister Denis Naughten says its a case of Europe attempting to dictate Irish tax law.
He says the Government should appeal the ruling.
"I think the Government are right to appeal it. I think there is a broader issue here of the Commission dabbling into Ireland's ability to actually set corporate tax rates and I think it is important that the Irish Government… appeal this decision."
Update 4.50pm: The Cabinet has failed to reach a decision on appealing the Apple tax ruling, and Ministers are to meet again on Friday.
Independent Alliance Ministers have moved towards agreeing to an appeal, but only if they get a recall of the Dáil.
While Fine Gael Ministers were clear that the ruling had to be appealed to the European Courts of Justice, Independents around the Cabinet table need convincing.
However Independent Alliance Ministers Shane Ross and Finian McGrath have reportedly signalled they would support a decision to launch an appeal if the Dáil is recalled and debates a motion on tax policy that is strongly worded.
In a statement, Children's Minister Katherine Zappone says she welcomes the fact the Cabinet did not rush to a decision, adding she believes there should be greater scrutiny by the Oireachtas to ensure no such issues arise again.
A Cabinet statement said the Government had a thorough discussion of the European Commission decision with regard to Apple.
The statement said: "Cabinet received a detailed briefing from Minister Noonan. Ministers also had an opportunity to examine the full text of the European Commission decision, which is a lengthy and complex document.
"Following the discussion, it was agreed to adjourn the meeting to allow further time to reflect on the issues and to clarify a number of legal and technical issues with the AG’s Office and with officials.
"The Government meeting will resume on Friday at 11am to make a decision on the matter."
Update 1.05pm: Ryanair boss Michael O'Leary has weighed into the tax dispute between Apple and the European Union, saying the Irish government should write a letter to the EU telling them to "f**k off".
Dubbing the EU's ruling "bizarre", Mr O'Leary said: "One of the fundamental principles of the European Union is that each country has its autonomy to make its own tax decisions.
"Frankly the Irish government should turn around - they shouldn't even appeal the decision - they should just write a letter to Europe and tell them politely to f**k off.
"The idea that you have the state aid mob - who've had more court verdicts overturned than any other department in Europe in the last 20 years - come along 10 years after the fact and say, 'no we didn't like that, we think you should have done something else', is frankly bizarre."
Apple is set to challenge the decision, and Mr O'Leary added: "I think there's no chance of this surviving a court ruling in Europe. There's certain things that Europe has no competence in."
Update 12.25pm: Foreign Affairs Minister Charlie Flanagan has described the European Commission's €13bn Apple tax decision as "baffling", writes Elaine Loughlin of the Irish Examiner.
Cabinet is today meeting to discuss the ruling which has a caused major split between Fine Gael and members of the Independent Alliance who have differing views on the ruling.
"There are a number of glaring inconsistencies in what the Commission says," he said.
Speaking before the Cabinet meeting Mr Flanagan said: "I fundamentally disagree with the analysis of the European Commission, the Irish Government takes this most seriously."
He said the government had co-operated fully with the Commission in its investigation and added that "we have always fully enforced our tax laws".
Speaking of the differing views held by members of the Independent Alliance he said: "Of course we have to realise political reality not only do we not have a Fine Gael government, but we don't have a majority government.
"So this issue will be subject to discussion, I hope we will be in a position to have an agreed decision, that's what the Cabinet meeting is all about, to facilitate the reaching of a certain consensus."
Update11.15am: Minister for Jobs Mary Mitchell O'Connor has insisted Ireland will appeal the European ruling forcing it to recoup back taxes from Apple.
Her comments come despite Independent ministers still being unclear about whether to support an appeal against the €13bn ruling.
Minister Mitchell O'Connor said there should be "no question marks" about Ireland's 12.5% corporate tax rate.
She said: "We will be appealing it. It's really important to send out the message loud and clear that there was no criticism on the 12.5% corporation tax (and) no levies or fines imposed on Ireland. Ireland is open for business."
Meanwhile, economist David McWilliams has said the ruling is "political".
"It's about the US on one hand and the EU on the other. Ireland got caught in the middle," he said.
On his way into Government Buildings this morning, the Taoiseach Enda Kenny said everybody needed time to properly digest the 150-page ruling, hinting a decision on the appeal may not be made today despite expectations to the contrary.
Update 11am:The Government body in charge of attracting foreign investment into Ireland has added to the criticism of the European ruling on Apple.
The IDA's chief executive Martin Shanahan said that interfering with our tax laws would make the IDA's job much harder.
"This is a situation where the Commission is retrospectively imposing its 2016 view of tax on an historic international tax context in Ireland. It's very unhelpful," he said.
Minister for Public Expenditure and Reform Paschal Donohoe has said Ireland must be allowed set its own taxes, as the fallout continues from the Apple tax ruling.
Minister Donohoe said the Government was not complicit in tax avoidance following the European Commission's ruling yesterday that Apple owes €13bn in back taxes.
The tech giant could be forced to pay Ireland up to €19bn to Ireland when interest is taken into account as a result of the decision.
The cabinet is set to hold a special meeting this morning to discuss the ruling. It is expected that the Government and Apple will both lodge formal appeals.
Minister Donohoe said all Ministers, including those in the Independent Alliance, would be given the opportunity to understand the issue at this morning's gathering.
"The heart of all of this is Irish jobs, and the right that a country has to have the ability to set its own tax policy in an area like this and trust its national institiutions to implement their law," he said.