Reynolds, 84, shared a message on Facebook on Tuesday morning, shortly after a family spokesman confirmed to ABC News that Fisher died.
"Thank you to everyone who has embraced the gifts and talents of my beloved and amazing daughter," Reynolds wrote. "I am grateful for your thoughts and prayers that are now guiding her to her next stop. Love Carrie's Mother"
"We just need to tell everybody to keep the prayers up because the doctors are doing everything they can for her right now," he said. "She's a real survivor and always has been, and I would expect the best from this. That's how we're approaching it."
On Saturday, Reynolds wrote on her Facebook page that Fisher was "stable," although her medical condition was unclear.
"To all her friends and fans, I thank you all for your prayers and good wishes," she wrote.