WASHINGTON — An extraordinary brief filed last week in the Supreme Court has put the Justice Department in an awkward spot.

The brief said federal prosecutors had violated the Constitution by failing to turn over evidence about a key witness.

“Such an approach,” the brief said, “contributes to a harmful notion that the criminal justice system is a game, and that victory rather than justice is a prosecutor’s goal.”

The argument itself is not unusual. But the people making the argument are.

They include some 20 former Justice Department officials, including Michael B. Mukasey, who served as attorney general in the Bush administration. Seth P. Waxman, who was solicitor general in the Clinton administration, represents the former officials.