European Competition Commissioner Margrethe Vestager has rejected claims by Apple Chief Executive Tim Cook that figures suggesting the company had paid only 0.005% in tax in 2014 were false.
Speaking at a news conference in Brussels, Ms Vestager said the findings of the commission's investigation into Apple's tax dealings in Ireland were based on figures provided by the company itself, as well as figures released during the US Senate hearings into Apple in 2013.
She also rejected claims by Mr Cook that the commission's decision was "political".
"This is a decision based on the facts of the case, looking into Apple Sales International, how they are arranged within Ireland, and the profits recorded there - how they are taxed.
"The enforcement part of the competition portfolio does not really fit into any political picture.
"It fits into the [EU] treaty, because by the treaty we have these obligations."
In an interview with RTÉ News, Mr Cook said the decision was maddening and was not based in law or in fact and the scale of the tax bill to be repaid has shocked the company.
In relation to Mr Cook's rejection of the investigation's findings, Ms Vestager said that the difficulty in discovering details about so-called tax rulings, or letters of comfort from the tax authorities to companies, meant there was a strong case for greater transparency.
"Our investigation is not into the Apple Corporation as such. It is into Apple Sales International and Apple Operations Europe and that is where the figures of - in some years - 0.005% are accurate."
She said: "We take independent decisions which are fact based."
Asked if she believed the Irish government knew that the tax arrangements between Ireland and Apple were allegedly illegal, the commissioner said she did not know what the Irish authorities "knew or thought or felt" about whether the alleged tax ruling of 1991 was legal or not under EU state aid rules.
Referring to the allegation of a "head office" connected to both Irish subsidiaries which had no premises or employees, she said: "How do they make so much money, and if they make so much money how come they don't pay tax?"
The commissioner said that the delay in publishing the redacted version of the full report, thought to run to 130 pages, was due to confidentiality concerns by Apple.
"If I had my way the report would have been published yesterday."
Ms Vestager said she would meet US Treasury Secretary Jack Lew in Washington in September to further discuss the Apple tax case.
Meanwhile, the French Finance Minister has said the commission was right to order Apple to pay the €13bn in back tax.
"The European Commission treated it as abnormal state aid ... the European Commission is doing its job," Michel Sapin told a news conference.
"It's normal to make Apple pay normal taxes."
The United States has accused the European Union of grabbing revenue intended for US coffers with the decision, comments that could cause friction at an international summit in China next week.
Ryanair CEO Michael O'Leary, meanwhile, has said Ireland has tax autonomy and should not be told by the EU "who we tax and how we tax".
Mr O'Leary said Ireland should tell the European Commission "to go to hell".
O'Leary: Govt should tell EU to go to hell over Apple pic.twitter.com/5fHl0jycZH— David Murphy (@davidmurphyRTE) September 1, 2016
He attacked the decision of the Commission's Competition Directorate to make an announcement on tax policy, saying "one of the cornerstones of the EU is each country has tax autonomy".
Claiming Ireland had no chance of getting €13bn from Apple, Mr O'Leary added that Ireland should not "roll over" on the issue.
The Independent Alliance is meeting today to discuss whether the Government should appeal the ruling.