Apple has lost its final attempt to overturn a judgment that it broke antitrust laws by conspiring to raise ebook prices in the iPhone maker’s latest bruising encounter with the US judicial authorities.

The US Supreme Court rejected the company’s bid for an appeal against lower court rulings that it engaged in “marketplace vigilantism” against its rival Amazon and “unreasonably restrained trade” by creating a “cartel” with publishers to control ebook prices.

The ruling comes as the company begins a long fight with the US Department of Justice over whether it can be forced to help investigators break open an iPhone belonging to one of the killers in the San Bernardino terrorist shootings in December.

It is also a blow to Tim Cook, the chief executive, who has called the case “bizarre” and has defended deals struck by his predecessor Steve Jobs, and by Eddy Cue, Apple's internet services head. 

“We’ve done nothing wrong there and so we’re taking a very principled position on this,” Mr Cook said in an interview in 2013, just before the case came to court. “We’re not going to sign something that says we did something we didn’t do. So we’re going to fight.”

Apple must pay $400m in compensation to people who bought ebooks through its iBooks store, under the conditional settlement agreed in July 2014. Five publishers have already paid out $166m as part of their 2013 settlement. 

But, on Monday, the Department of Justice said that the company and book publishers had engaged in “cynical misconduct” as they worked in concert against the lower prices imposed by Amazon's Kindle store. 

“Apple’s liability for knowingly conspiring with book publishers to raise the prices of ebooks is settled once and for all,” Bill Baer, assistant attorney-general of the Justice Department’s antitrust division, said in a statement. “And consumers will be made whole.”

Customers who bought books at higher prices will be repaid in store credits. 

The US government accused Apple of being the “ringleader” in a conspiracy with the world's largest book publishers to raise ebook prices using its iPad, at a time when Amazon’s Kindle dominated the market. 

©Reuters

Apple's Tim Cook

Whereas Amazon set ebook prices for the Kindle store, Apple introduced the “agency pricing” model with its iBooks system, allowing publishers to decide how much to charge. 

The 2013 trial revealed that a string of emails were sent by Jobs and Mr Cue to publishing industry executives during their negotiations over iBooks. In one message, the Apple co-founder told James Murdoch of News Corp that Amazon's pricing model was “not sustainable” and that Apple was “the only other company currently capable of making a serious impact” in the ebooks market. 

“Dynamic, disruptive entry into new or stagnant markets — the lifeblood of American economic growth — often requires the very type of vertical contracting and conduct” that the courts had blocked in their earlier rulings, Apple's legal team argued last year as it sought to take the case to the Supreme Court. 

Apple did not respond to a request for comment on Monday.