The Oscar winner, 89, stopped by The View on Wednesday where she was asked about Brando "constantly" cheating on her during their on-and-off relationship by co-host Joy Behar.
"I found lingerie in his house and, of course, I was heartbroken, and I went home in tears — really, I was naïve — and I was angry too, just furious. The next day, the phone rings, and I hear 'Miss Marina?' I said, 'Uh, yeah?' " she recalled. " 'This is Colonel Parker, my client is Elvis Presley, and Elvis spotted you at the 20th Century Fox commissary, and he liked what he saw.' "
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"I said 'Oh?' and he said, 'And he would like very much to meet you. Would you like to meet him?' " the West Side Story star continued, adding, "And I thought of those panties, and I said, 'Yes, I would!' "
Moreno said that she "dated [Elvis] several times" and that she found him to be "sweet but boring."
"He was sweet, but he was a country boy. So anyway, when [Brando] found out, it didn't take long. He started to throw chairs. He was so angry. It was wonderful. And I just sat there as he threw chairs and carried on," Moreno said, crossing her arms and pretending to look at her nails as she mimicked being unfazed by Brando's reaction.
Moreno and Brando met when she was 22 on the set of the Napoleon biopic Désirée.
The actress's life, career, and tumultuous relationship with Brando were detailed in the documentary Rita Moreno: Just a Girl Who Decided to Go for It, which debuted at the 2021 Sundance Film Festival earlier this year. The documentary is now streaming on Netflix.
"He was the daddy that I couldn't please. I didn't know that, I wasn't aware of that at all," Moreno said in the documentary. "But he was the one I wanted to please, he was the one I wanted to be married to."
In 2017, Moreno told PEOPLE Brando was the "lust" of her life and revealed she kept a photo of The Godfather star in her bedroom.
"Why that picture of Marlon Brando? Because he was a big love of mine in my life," Moreno said at the time. "This one, it almost seems like a vignette out of a movie, so that's why it's there. He was the lust of my life and that over there is the love of my life," admitted Moreno, gesturing to a framed photo of her with her husband, pictured in an embrace, in silhouette.
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In her 2013 memoir, Rita Moreno, the EGOT winner wrote about her relationship with Brando in detail — an emotionally wrought, turbulent time in her life that included an abortion and a suicide attempt.
Moreno credits therapy, leaving Hollywood and returning to the New York stage with helping her get through that difficult time, but says that marrying her late husband Leonard Gordon in 1965 played the biggest role in her recovery.
"We balance each other," she told PEOPLE in 1975. "I am not exactly Mrs. Good Housekeeping, although I love to cook, bake, even iron, but only because it's not mandatory."
20th Century-Fox/Getty Marlon Brando and Rita Moreno in Désirée
Years later, Brando was welcomed into Moreno and Leonard's family as a close friend.
"[My daughter] came home from school one day and found him playing the congas in our living room," Moreno told PEOPLE. "She called him 'the man with the drums.' "
Moreno can next be seen in Steven Spielberg's adaptation of West Side Story, which debuts on Dec. 10, just one day before her 90th birthday.