Plaintiffs who sued and won over Apple Inc in 2013 over an e-books price fixing scheme wants the global telecom giant to pay a total of $840 million in damages.

In July 2013, the U.S. Justice Department won the antitrust lawsuit it slapped against Apple and sought $280 million in damages. But now they want that amount tripled through a new lawsuit slapped against the Cupertino company on Friday.

Steven Berman, the attorney leading a class action against Apple, filed the claim in New York on behalf of e-book customers in 33 states.

The complainants argued they're entitled to triple the damages under antitrust law based on the court's ruling that Apple was "conclusively proven" to have orchestrated a conspiracy to fix prices.

They said Apple met directly with publishers and presented an agency model scheme, entailing publishers rather than retailers, to set the price for e-books. Amazon and other retailers would then be either forced to raise prices or stop supplying e-books, which indeed happened.

According to the Guardian Liberty Voice, a company found guilty of violating the U.S. antitrust laws may have to pay a threefold damage.

"Based on the amount of the cash Apple had at the end of 2013, the amount is equivalent to 0.5 per cent of the $158.8 billion in cash," the online portal said.

In 2012, Apple's sales of e-books, music, movies, software and services reached $12.9 billion, representing 8.2 per cent of its total revenue.

US District Judge Denise Cote, who tool and ruled over the case in July, will be the same judge who will preside over the new lawsuit.

She said she will hold a trial this year, 2014, on the damages sought by the states.

Apple introduced e-books in 2010 to boost the appeal of the newly unveiled iPad tablet as a reading device, according to Bloomberg.