One of Petty's daughter posted pictures of Monday's private memorial event and of the lotus-shaped archway to the Self-Realization Fellowship Lake Shrine, near the Pacific coast in Los Angeles County.
Petty, who died a week earlier at age 66 after suffering a cardiac arrest, in his later years practiced transcendental meditation, seeing a way to control anger after earlier abusing heroin and other drugs.
Daughter AnnaKim Violette Petty shared a series of images on Instagram including one of a small bouquet of flowers with the words, "You belong somewhere you feel free," a line from Petty's song "Wildflowers."
She also shared quirkier thoughts including an image from Petty's memorable "Alice in Wonderland"-themed video for "Don't Come Around Here No More," with the rocker surrounded by three platinum-blonde women in skin-tight black-and-white dresses.
"May you be protected by the hottest vixens in heaven," his daughter wrote, adding in a likely allusion to his song "The Waiting": "Heaven is something u feel."
Petty's representatives did not immediately comment on whether there would be an additional public event or a permanent marker for his remains.
The Florida-born rocker -- whose string of hits included "I Won't Back Down, "Free Fallin'" and "American Girl" -- died days after completing a tour to mark 40 years with his band The Heartbreakers.
Harrison, the former Beatle who joined Petty in the Traveling Wilburys supergroup, was cremated at the Los Angeles shrine in 2001. The remains of Harrison, who was passionate about Hindu spiritualty, were then scattered in the holy waters outside of Varanasi, India.
The Self-Realization Fellowship Lake Shrine features a public garden with swans, wildlife and symbols of the world's major religions, with space for silent meditation and reflection.
The site was founded in 1950 by Paramahansa Yogananda, the Indian spiritual teacher and author of "Autobiography of a Yogi" who was instrumental in bringing Eastern meditation to the United States.
The shrine, which was also a favorite retreat for Elvis Presley, features a sarcophagus that holds some of the ashes of Mahatma Gandhi, India's slain independence hero and apostle of non-violence. — Agence France-Presse
