Mr. Domingo, who has been married for more than 50 years, said in the statement that “the allegations from these unnamed individuals dating back as many as 30 years are deeply troubling, and as presented, inaccurate,” but added that “it is painful to hear that I may have upset anyone or made them feel uncomfortable — no matter how long ago and despite my best intentions.”

He said that “the rules and standards by which we are — and should be — measured against today are very different than they were in the past” and pledged to hold himself “to the highest standards.”

Mr. Domingo occupies a unique position in the opera world. After shooting to fame as a star tenor — then reaching a far broader global audience as one of the Three Tenors, alongside Luciano Pavarotti and José Carreras — he also became a conductor; founded the prestigious young artist competition Operalia; and began adding managerial positions, becoming the general director of Washington National Opera and then the Los Angeles Opera, a position he still holds. He also continues to have a prolific singing career in baritone roles.

These activities have made him one of the most influential figures in opera.

The Los Angeles Opera said in a statement that it would engage an outside counsel to investigate what it called “the concerning allegations” against Mr. Domingo.

“Plácido Domingo has been a dynamic creative force in the life of L.A. Opera and the artistic culture of Los Angeles for more than three decades,” the opera company said in a statement. “Nevertheless, we are committed to doing everything we can to foster a professional and collaborative environment where all our employees and artists feel equally comfortable, valued and respected.”