She wrote: "Dear Paris Jackson, don't let bullies to let you down. We believe in you!! Stay strong, Please."
Demi previously admitted she signed a “no suicide contract” after going through some tough times when she first found fame at the age of seven.
She said: “The principal called my parents and made me sign this suicide contract saying that I would not kill myself. They weren’t expecting that so young."
Following the incident, Paris' grandmother Katherine Jackson insists her granddaughter was "physically fine"
She said in a statement: "Paris is physically fine and getting appropriate medical attention.
"Being a sensitive 15 year old is difficult no matter who you are. It is especially difficult when you lose the person closest to you.
"Please respect her privacy and the family's privacy."