BRUSSELS—A war of words has erupted between Europe’s competition chief and Apple CEO Tim Cook after Ireland was ordered to reclaim €13 billion (£11.1 billion/$14.5 billion) in back taxes from the company.

Cook, in an interview with the Irish Independent, labelled Brussels' competition chief Margrethe Vestager’s decision as “total political crap.” He claimed Ireland was being "picked on" and that he hoped to see the Irish government launch an appeal against the ruling.

On Tuesday, Vestager said that the European Commission’s two-year investigation had found Apple guilty of receiving illegal state aid from Ireland thanks to so-called sweetheart tax deals in 1991 and 2007. She said that Ireland allowed Apple to pay an effective corporate tax rate of one percent on its European profits in 2003, down to as low as 0.005 percent in certain years.

Apple, in a statement on Wednesday, said that the "number quoted by the European Commission is extremely misleading and deceptive." It added:

We paid $400 million in taxes in Ireland in 2014—considerably more than the commission’s figure suggests. We were certainly one of the largest corporate taxpayers in Ireland that year, if not the largest. In addition, we paid $400 million of current US taxes on those profits, bringing total current taxes paid to $800 million. Most importantly, the commission completely ignores the fact that the vast majority of those profits was subject to US taxation. Apple also accrued several billion dollars in US deferred taxes on those profits earned in 2014.

Vestager refuted that claim when quizzed by reporters on Thursday. "This is a decision based on the facts of the case. The figures that we used in our decision are the figures that we got from Apple themselves," she said.

"There are very, very few figures in the public domain. More transparency would be a good thing, for example, a country by country reporting. If it was up to me, the non-confidential version of the decision would have been published yesterday, because that is another way of enabling everyone to see what we have decided and on what basis we have made this decision. Right now the ball is in the hands of Apple and Ireland."

She also rejected Cook’s claim that her decision was politically motivated. Vestager said: "The enforcement part of the competition portfolio does not really fit into any political picture. Even if it weren’t like this, we always have the courts to keep us in line. Because I don’t think the courts will hear any political opinions or feelings, they want the facts of the case and that is what we have to produce."

Apple has said it plans to appeal against the decision. However, despite previously insisting that Ireland's government would similarly challenge the commission's ruling in the courts, an agreement to do so wasn't made by the Irish cabinet during a special meeting convened on Wednesday.

The US has also weighed in on the case. Last week the treasury department warned that it would "consider its options." On Wednesday, treasury secretary Jack Lew said that he was concerned that the case was an attempt to reach into income that ought to be taxed in the US.

Ars asked Vestager to respond to Lew's claims about the distribution of Apple's coffers. The commissioner said: "The Apple case is about profits made by sale in Europe so obviously it is a question of tax being paid in Europe. It is a European matter and a matter for state aid rules." She added that she was looking forward to meeting Lew in person in Washington later this month.

Meanwhile, Brussels' competition officials continue to investigate a similar case about Amazon's tax arrangements in the European Union.