Apple’s chief executive on Thursday stepped up the outrage over Europe’s demands that it pay a record $14.5 billion in unpaid taxes, calling the decision “maddening” and expressing confidence it would be overturned.

Timothy D. Cook, the Apple chief, stridently defended the company’s tax practices in Ireland, countering European officials’ ruling this week that the Irish government had provided illegal incentives, which allowed the technology giant to pay essentially nothing some years. In an interview with the Irish broadcaster RTE, Mr. Cook said the company paid its fair share in Ireland, the United States and elsewhere.

Mr. Cook also noted that Apple planned to send some of its enormous amount of cash overseas back to the United States next year, although he did not specify how much. Those international reserves have been particularly divisive as they remain out of the reach of American tax authorities.

“The finding is wrongheaded,” Mr. Cook told RTE. “It’s not true — there wasn’t a special deal between Ireland and Apple.”