The email from Mr. Egert, who declined to comment, criticized whoever divulged the specifics of the investigation, saying that they had broken an internal agreement to keep the details confidential. Earlier, union officials had told members that some of the women who had spoken with investigators had insisted on confidentiality, fearing reprisals from the industry. (The A.P. did not publish any names of women who had not already gone public.)

“As a result of their actions, A.G.M.A. has lost $500,000 that not only would have covered the costs of the investigation,” the email said, “but also would have funded an extensive sexual harassment prevention training program that is so desperately needed in our industry.”

Nancy Seltzer, a spokeswoman for Mr. Domingo, disputed that account, and said that “what is truthful is we are in ongoing discussions with the union on how to move forward and nothing is off the table.”

Publicly, Mr. Domingo, 79, a famed tenor who held leadership positions at the Los Angeles Opera and the Washington National Opera, issued his fullest apology yet. “I have taken time over the last several months to reflect on the allegations that various colleagues of mine have made against me,” Mr. Domingo said in a statement on Tuesday. “I respect that these women finally felt comfortable enough to speak out, and I want them to know that I am truly sorry for the hurt that I caused them.”

Two of the women who went on the record to The A.P. to accuse Mr. Domingo of misconduct and harassment, Patricia Wulf and Angela Turner Wilson, said in a statement through their lawyer that they believed he should be expelled from the union.

Debra Katz, the lawyer representing them, said in an interview that she was “distressed” to learn about the union’s financial talks with Mr. Domingo.