Mr. Schmidt would not comment beyond an interview with ABC, according to his lawyer, John Manly.

Mr. Manly also represents about 200 accusers of Dr. Lawrence G. Nassar, the former American women’s gymnastics team doctor, who is expected to spend the rest of his life in prison after being convicted of serial sex abuse. Mr. Manly said in a statement that Mr. Schmidt’s case was another “sad example of the culture of child abuse that is rampant in our Olympic sports programs.”

U.S. Figure Skating and the rinks where Mr. Callaghan taught “ignored complaints against him for years,” Mr. Manly said in the statement, accusing the defendants of concealing from Mr. Schmidt’s parents and the authorities information that Mr. Callaghan might have abused skaters.

“If they had done their legal duty in 1999 and reported Callaghan to the police, our client and other children could have been protected from this monster,” Mr. Manly said.

U.S. Figure Skating said in a statement that it did not comment on pending litigation. But the federation added that it “fully supports all victims of sexual abuse and misconduct and encourages anyone who has been abused or suspects abuse or misconduct to immediately report it to local law enforcement, the U.S. Center for SafeSport or U.S. Figure Skating.”

In March 2018, Mr. Callaghan was suspended from the sport. He was coaching in Florida at the time and has previously denied any wrongdoing.

The suspension resulted from a complaint made to SafeSport by Craig Maurizi, 56, a prominent coach who was a former student and coaching partner of Mr. Callaghan’s. In 1999, Mr. Maurizi told The Times that Mr. Callaghan had engaged in inappropriate sexual conduct with him for a number of years, beginning when he was 15.

The accusations were dismissed at the time by U.S. Figure Skating because they had not been levied within a required 60-day period after the abuse allegedly occurred. Mr. Maurizi’s charges received renewed scrutiny after SafeSport decided to investigate.