NEW YORK (Reuters) - Volume in Barclays PLC's (>> Barclays PLC) private U.S. trading venue, also known as a "dark pool," fell by more than a third after New York's attorney general filed a lawsuit accusing the British bank of giving an unfair edge to high-speed traders, according to data released on Monday.

The number of shares traded in Barclays' LX, an alternative trading system or dark pool, dropped about 37 percent in the week of June 23 to around 197 million shares, from around 312 million shares the week before, according to a report by the Financial Industry Regulatory Authority. The report from FINRA, Wall Street's self-funded regulator, included only the most widely traded securities.

Dark pools are broker-run trading venues that let investors trade shares anonymously and only make trading data available afterwards, reducing the chance of information leaking about trade orders. The lack of transparency has drawn the scrutiny of regulators.

New York Attorney General Eric Schneiderman said on June 25 that he had evidence that Barclays staff had falsified marketing materials and misled big institutional clients in an effort to expand its dark pool and increase revenues. He accused the British bank of giving an edge to brokers and proprietary trading firms that use aggressive high-frequency trading strategies, while telling other clients it was protecting them from such tactics.

Deutsche Bank (>> Deutsche Bank AG), Credit Suisse (>> Credit Suisse Group AG), Royal Bank of Canada (>> Royal Bank of Canada), and Investment Technology Group (>> Investment Technology Group) were among several brokers and banks that said they had stopped routing orders to Barclays' dark pool after the securities fraud lawsuit was filed.

For the week of June 23, Barclays' dark pool was the fifth-largest in the United States, down from the second largest the week before. Dark pools run by Credit Suisse, UBS (>> UBS AG), Deutsche Bank and Bank of America's (>> Bank of America Corp) Merrill Lynch had more volume.

In early June, dark pool operator Liquidnet paid $2 million to the U.S. Securities and Exchange Commission to settle charges that the electronic trading network had improperly used its subscribers' confidential trading information to market its services. On July 1, Goldman Sachs (>> Goldman Sachs Group Inc) agreed to pay an $800,000 fine to FINRA to settle a case over pricing rule violations in its dark pool.

(Reporting by John McCrank; Editing by Jan Paschal)