The girl allegedly told her stepfather, Shelton Ray, that she stabbed the toddler, Sasha, The Atlanta Journal-Constitution reported.
Prosecutors did not speculate at Tuesday's hearing on what the motive for the crime could have been. Haneefa Ray, mother of both girls, cried, while her husband called "We love you" to his stepdaughter.
Sasha died Monday night at the family home in DeKalb County in the Atlanta area. Ray found his daughter's bloody body in the back yard after the older sister reported Sasha was missing.
The 13-year-old had been babysitting her younger siblings. While her parents were out, a neighbor called them to tell them a boy was visiting their daughter and then, at the Rays' request, went to the house to tell the boy to leave.
Homicides in which both victims and perpetrators are juveniles are unusual, with an average of just over 100 a year in the United States in recent years. Martha Grace Duncan, an Emory University law professor, said juries are often harshly inclined toward children charged with homicide, but a defense lawyer, Jimmy Berry, said they are also more likely to accept that a child could be mentally ill.