The 84-year-old star posted a statement on Facebook thanking fans for their prayers and support following Carrie's death.
"Thank you to everyone who has embraced the gifts and talents of my beloved and amazing daughter.
"I am grateful for your thoughts and prayers that are now guiding her to her next stop. Love Carries Mother," Reynolds wrote.
Reynolds and her then-husband, musician Eddie Fisher, welcomed their daughter on October 21, 1956. The "Singin' in the Rain" actress is also the mother of Carrie's brother, Todd Fisher.
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The actresses' half-sister Joely Fisher also shared an emotional post following the tragic passing of her big sister.
"Breaking my silence with a broken heart...The Unfathomable loss...The earth is off its axis today...How dare you take her away from us," Joely wrote alongside a photo of the pair embracing each other.
During Fisher's subsequent hospitalization after suffering a heart attack, Joely continued to thank fans for their ongoing support.