Investigations by the magazine “uncovered very unpleasant incidents, which are completely intolerable and which we regret greatly: Some individuals have behaved very badly,” the academy said in a statement. “The students who were subject to physical or emotional abuse have our deepest sympathy,” it added.

Students said that Bella Ratchinskaia, a teacher at the school, at times went beyond the limits of normal practice during ballet classes, roughly forcing their limbs into position or scratching them as she adjusted their bodies, sometimes drawing blood. André Comploi, a spokesman for the State Opera, said that Ms. Ratchinskaia, who previously worked at La Scala in Milan, was dismissed in February.

Ms. Ratchinskaia did not reply to a request for comment but said in a statement provided by the academy: “Contact is a part of the training in this profession — it is necessary to touch to make corrections in ballet classes, and this is done all over the world. To the students who I have hurt, I apologize sincerely. I never injured anyone deliberately, and it was never done maliciously.”

Another teacher who was accused of sexual assault was suspended on Monday pending an investigation by Austrian prosecutors. According to Sharon Booth, a former teacher who said she had spoken with the student involved, the teacher is accused of trying to get the student, a boy who was 16 at the time, to masturbate him. Mr. Comploi said that the teacher denies the allegation.