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The 27-year-old actress has been in various hospitals since she was placed under an involuntary psychiatric hold in July, and her mother Lynn Bynes says her fans' support is helping her to get better.
She told People magazine: "Both my husband and I love Amanda very much and we know that she will get through this situation.
"We appreciate everyone's heartfelt support and we hope that she can get some privacy and the respect she deserves during this trying time."
Lynn did not address allegations that the Easy A actress was formally diagnosed with schizophrenia and bipolar disorder recently.
But she said: "Please know that neither myself or other family members have ever released any information regarding her treatment or diagnosis. We truly believe in keeping our daughter's situation private for now."
Amanda was moved to The Canyon treatment facility in Malibu three weeks ago after spending two months at UCLA Medical Center.
Lynn was granted a temporary conservatorship over her daughter in August, shortly after the actress was hospitalised after she set a small fire in the driveway of a stranger's home in Thousand Oaks, Los Angeles.
