NEW YORK — The European Union on Tuesday ordered Ireland to collect $14.5 billion in unpaid taxes from Apple, a record penalty that worsened tensions with the United States over the bloc’s crackdown on sweetheart deals with global multinationals.

Europe’s competition enforcer said Apple’s illegal deals with the Irish government allowed the technology giant to pay virtually nothing on its European business in some years. The arrangements enabled Apple to funnel profit from two Irish subsidiaries to a “head office’’ with “no employees, no premises, no real activities,’’ the commission said.

By doing so, Apple paid only 50 euros in taxes for every 1 million euros in profit during 2014. As part of its ruling, Europe demanded that Ireland recoup 10 years’ worth of back taxes, some 13 billion euros, or about $14.5 billion, plus interest.

The amount is a drop in the bucket for Apple, which has a total cash pile of more than $230 billion. Even so, the company described the order as a “devastating blow’’ to the rule of law. The US Treasury Department said it jeopardized “the important spirit of economic partnership between the US and the EU.’’

Since taking over as competition commissioner, Margrethe Vestager has made tax avoidance a central focus, a campaign that has also ensnared Starbucks in the Netherlands, Amazon in Luxembourg, and Anheuser-Busch InBev in Belgium. The US Treasury, one of the most vocal critics of these moves, has said Europe is overstepping its power, unfairly targeting US companies and hurting global efforts to curtail tax avoidance.

The US government is an unlikely advocate. Politicians have berated Apple for paying too little by setting up complex and opaque tax structures. Officials have hit back against corporate mergers that allowed companies to move their headquarters to such places as Ireland to take advantage of lower tax rates.

But the positioning in the Apple case reflects a political tug of war over big profitable companies, their potential tax bounty, and the rights to regulate them.

“US companies are the grandmasters of tax avoidance,’’ said Edward D. Kleinbard, a professor at the Gould School of Law at the University of Southern California and a former chief of staff to the congressional Joint Committee on Taxation.

“Nevertheless, because of the nature of US politics,’’ he said, the Apple case “will be framed by the US as Europe overreaching and discriminating against ‘our team.’ ’’

Since early this year, Vestager and Jacob J. Lew, the US treasury secretary, and their teams have met regularly to discuss Europe’s tax investigations. Lew visited Brussels in July to put forward the US perspective.

Last week, the Treasury Department released a report criticizing any moves to recoup back taxes from US companies. Politicians also chimed in after the Apple decision.

Senator Chuck Schumer, Democrat of New York, called it a “cheap money grab’’ by the European Commission, “targeting US businesses and the US tax base.’’ The Senate Finance Committee chairman, Orrin G. Hatch, said the decision “encroaches on US tax jurisdiction.’’

Apple and Ireland had similar defenses.

Timothy D. Cook, chief executive of the technology company, said Europe’s ruling had “no basis in fact or in law’’ and called it an effort to “rewrite Apple’s history in Europe, ignore Ireland’s tax laws, and upend the international tax system in the process.’’ The company called the effective tax rate “a completely made-up number.’’

The Finance Ministry of Ireland said the commission’s decision would undermine a continuing global tax overhaul and create business uncertainty. The ministry said taxes were a “fundamental matter of sovereignty.’’

Ireland and Apple both said they intended to fight Europe’s decision, even though any appeal could take years.

The commission said the amount due in Ireland could be reduced if US authorities decided that Apple should have paid more tax in the United States. Other countries in the European Union could also potentially take a share.

“The ultimate goal should of course be that all companies, big or small, pay tax where they generate their profits,’’ the competition commissioner, Vestager, said at a news conference in Brussels on Tuesday. “We need a change in corporate philosophies and the right legislation to address loopholes and ensure transparency.’’

Although the United States appears to side with Apple and Ireland in this specific fight, the overall view is more complicated.

A US Senate committee said in 2013 that Apple had negotiated a special corporate tax rate of 2 percent or less in Ireland. While the committee did not accuse Apple of breaking any laws, lawmakers criticized the “gimmicks,’’ “schemes’’ and complex corporate structures that allowed the company to sidestep taxes. The public scrutiny and the emergence of previously confidential information about Apple’s tax arrangements, in part, helped spark Europe’s own investigation into the issue.

Apple and other companies have also faced criticism for keeping large reserves of cash overseas. The money is not taxed at home until it is brought back to the parent company in the United States.

Nonfinancial US companies hold a combined $1.7 trillion in cash overseas, according to the credit rating agency Moody’s. Just the international piece of Apple’s stash amounts to nearly $215 billion.