The ministry added that it had submitted all the information requested by the commission, and that it was cooperating fully with the investigation. “Luxembourg is confident that the allegations of state aid in this case are unsubstantiated,” it said.

The publication of the letter reflects heightened scrutiny of how low-tax nations in the European Union have helped large multinationals reduce their tax bills by billions of dollars, at a time when the budgets of larger countries, like France and Italy, are squeezed. The European Commission is already investigating the tax arrangements of Starbucks in the Netherlands, of Apple in Ireland and of a unit of Fiat in Luxembourg.

It is not illegal in the European Union to try to lure businesses with low tax rates. But offering special deals to companies that are not available to their competitors can amount to what is known as illegal state aid.

The Amazon tax investigation — made public last year — focuses on a deal the company struck with Luxembourg in 2003 to cap the amount of tax it paid through so-called transfer pricing, according to the commission. Luxembourg’s tax authorities took a mere 11 days to approve Amazon’s tax structure in the country, the commission noted.

Under the arrangements, most of the company’s European revenue was sent from one unit in Luxembourg to a separate subsidiary that was not liable to pay corporate tax in the country. That reduced the profit that the company generated from its European operations and cut its tax bill, the commission said.

Europe’s competition authorities have asked Luxembourg for more details on why it was “deviating” from international standards when handling this complex structure between Amazon’s two units.

They also called for more details of how royalty payments made between the units were structured, as the unit that received these payments was not subject to taxation in Luxembourg, according to the European Commission’s documents.