U.S. electronics giant Apple agrees to refund up to 400 million U.S. dollars to consumers if its appeal of an antitrust case is denied, according to court documents filed on Wednesday.

The U.S. Department of Justice filed a case in 2012 accusing Apple of conspiring with the country's five largest publishers to raise e-book prices with the intention to break the discount policy of Apple's rival Amazon for its e-commerce platform.

A New York federal district court ruled that Apple and the publishers had violated antitrust laws by fixing prices on July 10, 2013.

According to this finding, 33 state attorney generals launched a class lawsuit, claiming that the electronics giant should return as much as 840 million dollars to e-book consumers nationwide. The damages case is scheduled to be heard on Aug. 25.

Apple is appealing the decision, denying any wrongdoing. In a statement, it said that while waiting for the court to hear its appeal, it agrees to a settlement contingent on the outcome of the appeal, saying: "If we are vindicated by the appeals court, no settlement will be paid."

The attorney generals also confirmed in the court document that the amount of compensation Apple would pay would depend on the outcome of the appeal.

If the original court ruling that Apple violated antitrust laws is ultimately affirmed, e-book consumers nationwide will receive 400 million dollars.

However, if the appeals court reverses the original ruling and orders the liability to be retried, Apple will pay 50 million dollars to settle damage claims. If Apple is determined not to have violated antitrust laws, it will pay no damages.

New York Attorney General Eric Schneiderman called the settlement a major victory, which proves that "even the biggest, most powerful companies in the world must play by the same rules as everyone else."