Ms. Dushku soon shared what had happened with a friend, according to her post. That friend, a woman Ms. Dushku did not name, then visited the set and confronted Mr. Kramer. Later that day, Ms. Dushku broke her ribs in a failed stunt.
“Whereas he was supposed to be my protector, he was my abuser,” she wrote.
In an email to The New York Times on Tuesday, Mr. Kramer affirmed a denial he had previously given to Deadline Hollywood, an industry publication.
“These are outlandish, manipulated lies,” he told the publication. “I never sexually molested her. I’m sick to my stomach. It’s not true. I think she’s making this up in her imagination. This is all lies. Lies, lies, lies. This is just crazy. I treated her like a daughter. We all looked out for her.”
Mr. Kramer also disputed two other accusations of sexual misconduct, both published by Deadline and involving women who were not named.
In a statement provided to Deadline, Sue Booth-Forbes, who said she was Ms. Dushku’s legal guardian on the set, said she had reported Mr. Kramer’s behavior to an authority figure.
“I was met with blank stares and had the sense that I wasn’t telling that person anything they didn’t already know,” she said.
Ms. Dushku, she added, “was treated like one of the boys, not a 12-year-old girl.”
Ms. Dushku’s Facebook post sparked an outpouring of support from several of her “True Lies” co-stars.
Jamie Lee Curtis, who played her mother, said in a HuffPost piece that Ms. Dushku had told her of the assault a few years ago, and she praised her for coming forward.
“Eliza’s story has now awakened us from our denial slumber to a new, horrific reality. The abuse of children,” she wrote.
James Cameron, who directed the movie, reportedly said Ms. Dushku was “brave” for speaking up.
And the actors Tom Arnold and Arnold Schwarzenegger said on Twitter that they would have helped had they known.
“All of us would have done something,” said Mr. Schwarzenegger, who played her father in the movie. “I’m shocked and saddened for Eliza but I am also proud of her — beyond being a great talent and an amazing woman, she is so courageous.”
In her piece, Ms. Curtis noted the difficulties faced by child actors, who are often thrust into a world they may not be fully equipped to understand.
“I have wrestled with my role as a mentor, colleague, surrogate, and friend, and each relationship is individual and unique,” she said of working with child actors. “Are we really friends? Are we work mates? Children are not mature enough to recognize that subtle difference.”