By Christopher M. Matthews 

New York state's top prosecutor raised the pressure on Barclays PLC Wednesday, alleging the bank hasn't cooperated with an investigation into the activity of high-speed traders in its "dark pool" and naming specific employees who were allegedly involved in wrongdoing.

New York Attorney General Eric Schneiderman, who sued the British bank in June, said in an amended civil complaint Tuesday that Barclays had defied subpoenas seeking the testimony under oath of the two top executives running the bank's Equities Electronic Trading Division, which oversees its dark pool.

The complaint alleges the executives-- William White, head of electronic trading, and David Johnsen, head of product development--were directly involved in, and oversaw, much of what it calls fraudulent activity in the dark pool, which prosecutors say benefited high-frequency traders to the detriment of the bank's retail investors. Dark pools are electronic trading venues that don't post investors' buy and sell orders and report trades to the public only after they take place.

A Barclays' spokesman declined to comment on behalf of Messrs. White and Johnsen, both of whom are still employed at the firm. In a statement, the bank said the amended complaint "merely repackages the same flawed arguments that were in the original complaint. While we continue to seek to cooperate with the New York Attorney General in this matter, we will continue to defend vigorously against these allegations."

Mr. Schneiderman's office alleged in June that Barclays constructed its dark pool to benefit high-frequency traders while lying to its other clients by saying the pool was designed to protect them from high-frequency traders.

In July, the bank filed a motion with New York State Supreme Court seeking to dismiss the case, saying Mr. Schneiderman used misleading information and cherry-picked facts to support his allegation that the bank lied to its clients about the activity of high-speed traders in its dark pool. The bank said the case is "based on clear and substantial factual errors."

The suit roiled dark-pool trading, sparking other financial institutions that offer similar venues to review their operations. The opaque trading platforms have also drawn scrutiny from other regulators, including the Securities and Exchange Commission.

Wednesday's complaint, which must be approved by a judge to proceed, didn't substantially change the allegations against the bank, but provided more details about what prosecutors said is a "broad pattern" of wrongdoing.

According to the complaint, Barclays falsely represented to the public, and to the New York state court, that it had barred a high-frequency trading firm from its dark pool in June 2012. Prosecutors allege the firm, GTS Securities LLC, continued to trade millions of shares in the pool for more than a year after.

"GTS is confident that its trading activity is and has been fully compliant with regulatory rules and policies," a spokesman said, adding that GTS was never prohibited from trading in the Barclays dark pool for any period of time.

Prosecutors allege Barclays courted predatory high-speed firms, contrary to the firm's public statements that it wasn't soliciting such clients. According to a former unnamed Barclays director quoted in the complaint, "It's almost like they are building a car and saying it has an air bag and there is no air bag or brakes."

Write to Christopher M. Matthews at christopher.matthews@wsj.com

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