Domingo defended himself after several women, one of whom was identified, accused him of using his position as one of opera's most celebrated singers to pressure them into sexual relationships.
Eight singers and a dancer told the Associated Press that they were sexually harassed in incidents going back to the 1980s. One said Domingo had put his hand down her skirt while three said he had forcibly kissed them.
Some said they felt their careers had been damaged by rejecting his advances.
"The allegations from these unnamed individuals dating back as many as 30 years are deeply troubling, and as presented, inaccurate," Domingo said in a statement sent to AFP via his publicist.
"Still, 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 added.
The LA Opera, where Domingo has been director general since 2003, said in a statement that it would "engage outside counsel to investigate the concerning allegations."
"Placido Domingo has been a dynamic creative force in the life of LA Opera and the artistic culture of Los Angeles for more than three decades.
"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," it added.
Spanish-born Domingo was one of the most recognized opera stars of the 20th century, starring in the Three Tenors alongside Luciano Pavarotti and Jose Carreras.
In recent years, the long-time married singer has transformed himself into a baritone and still performs to packed audiences at age 78.
"I believed that all of my interactions and relationships were always welcomed and consensual. People who know me or who have worked with me know that I am not someone who would intentionally harm, offend, or embarrass anyone," he said.
"However, I recognize that the rules and standards by which we are -- and should be -- measured against today are very different than they were in the past," he added. (AFP)