(Adds comment from New York Attorney General, paragraphs 4-6)

By Saqib Iqbal Ahmed

NEW YORK, Jan 1 (Reuters) - New York Attorney General Eric Schneiderman on Thursday filed an amended lawsuit against DraftKings and FanDuel asking the daily fantasy sports companies to give back all the money they made in New York State.

The amended lawsuit asks the two companies to make restitution of all funds obtained from consumers in connection with alleged violations and seeks a civil penalty of up to $5,000 per case.

The lawsuit also asks that the two companies provide an accounting of the money they collected from consumers in New York who played any of their games.

"This filing, which follows a determination by the State Supreme Court that DraftKings and FanDuel have been running illegal sports betting operations, seeks appropriate fines and restitution from the companies," Schneiderman said in an emailed statement to Reuters.

"It should be no surprise that the amounts involved are substantial, given the skyrocketing size of these illegal gambling operations," he said.

In 2014, daily fantasy sports players in New York State wagered more than $25 million on DraftKings, according to the suit.

"Like the NYAG original complaint, it is based on the fundamental misunderstanding of fantasy sports competitions," David Boies, a lawyer for DraftKings, said about the revised complaint, in a statement.

DraftKings declined to comment specifically on the demand for restitution. New York-based FanDuel did not immediately respond to a request for comment.

The amended lawsuit is the latest twist in the fantasy sports companies' legal battle in New York to permanently continue doing business there.

FanDuel and DraftKings are engaged in a fight in court against New York state's top prosecutor, who says that the two companies are running illegal gambling operations and ordered them to stop taking bets in the state.

The daily fantasy sports companies, which contend that the games require skill, in December won a temporary reprieve that allows them to keep operating in New York until at least Jan. 4.

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The fantasy sports industry allows participants to assemble imaginary pro football, baseball, basketball and hockey teams from rosters of real players and to accumulate points based on how those players perform in actual games over the course of a season.

The daily versions allow fans to spend money on the game with a frequency that critics say is akin to sports betting. Purveyors of fantasy sports argue it is a skilled-based entertainment product, not wagering.

Boston-based DraftKings and FanDuel, both privately held, have valuations of more then $1 billion. High-profile investors have poured money into both.

FanDuel has more than 600,000 players in the state, about 10 percent of their users and DraftKings has more than 500,000 daily fantasy players in the state. New York has the most daily fantasy sports players of any state, according to Eilers Research. (Reporting by Saqib Iqbal Ahmed; Editing by Andrea Ricci and David Gregorio)