“It was meant to go to the descendants in the first place,” Ms. Head, who lives in Virginia, said in an interview on Friday.

The group has sent a letter to Federal District Judge Myron H. Thompson asking him to withhold a decision on the money until the organization has time to hire a lawyer and file documents in the long-running class action lawsuit over the study.

Fred Gray, a lawyer who heads the museum and represented study participants in the lawsuit, said he had not seen the Voice group’s letter, and declined to comment on its request. Mr. Gray has requested the money for the museum, the Tuskegee Human and Civil Rights Multicultural Center, which includes an exhibit about the syphilis study and a memorial to the men.

Beginning in 1932 in the impoverished, segregated South, government medical workers in rural Alabama withheld treatment from unsuspecting black men who had syphilis so that doctors could track the disease and dissect the men’s bodies afterward. The study was revealed by The Associated Press in 1972, and was ended. The surviving men sued, resulting in the settlement.

More than 6,000 heirs of the roughly 600 men involved in the study received settlement payments through the decades, court officials say, but an undisclosed amount remains in court-controlled accounts. Court officials say they cannot find additional descendants, if any exist. All of the men who participated in the study are now dead.