WASHINGTON — Apple Inc. must pay $450 million to end an antitrust suit after the US Supreme Court ­refused to question a finding that the company orchestrated a scheme to raise the prices for electronic books.

The justices, without comment, turned away an appeal by Apple, leaving intact a federal appeals court ruling favoring the US Justice Department and more than 30 states that sued.

The rebuff means Apple must comply with a settlement it reached with the states in 2014. The accord calls for Apple to pay $400 million to e-book consumers, $20 million to the states, and $30 million in legal fees.

Consumers who overpaid will get credits they can apply to future e-book purchases, the Justice Department said in a statement.

“Apple’s liability for knowingly conspiring with book publishers to raise the prices of e-books is settled once and for all,’’ said Assistant Attorney General Bill Baer, who runs the department’s antitrust division.

Government lawyers accused Apple of leading a price-fixing effort as part of the 2010 introduction of its iPad tablet and iBookstore feature. Apple was seeking to gain a foothold in a market dominated by Amazon.com Inc., which at the time treated best-selling books as loss leaders, selling them for $9.99.

A federal judge in Manhattan found that Apple persuaded five of the biggest publishers to shift to a system under which they, and not the retailers, would set book prices. The shift led to a 40 percent increase in the price of e-book bestsellers, US District Judge Denise Cote said.

Cote pointed to statements by ­Apple’s late founder, Steve Jobs. At the Apple event to introduce the iPad, Jobs was asked why someone would buy a book through iBookstore for $14.99 when the same item was available on Amazon for $9.99.

“Jobs paused and with a knowing nod responded, ‘The price will be the same,’ and explained that ‘publishers are actually withholding their books from Amazon because they are not happy,’?’’ Cote wrote.

Cote also ordered changes to Apple’s business practices and appointed a monitor to ensure the company’s compliance.

At the Supreme Court, Apple argued that its actions enhanced competition by providing consumers with a new e-book platform. The company said e-book prices have fallen in the years since the introduction of iBookstore.

“Following Apple’s entry, output ­increased, overall prices decreased, and a major new retailer began to compete in a market formerly dominated by a single firm,’’ the company said in its appeal.

Before signing the Apple settlement, the states and consumers recovered a total of $166 million in separate accords with the publishers — ­Hachette Book Group Inc., HarperCollins Publishers LLC, Simon & Schuster Inc., Pearson Plc’s Penguin Group, and the Macmillan unit of Verlagsgruppe Georg von Holtzbrinck GmbH.

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