Johannesburg - Marli van Breda, who survived an attack on her family in Stellenbosch, during which her parents and a brother were killed, is in a stable condition in hospital, the family said on Sunday.
"Marli is in a stable condition in the Medi-Clinic in Stellenbosch," the family said in a statement.
"No visitors are allowed at her bedside."
The Van Breda family were attacked in their home in the De Zalze Golf Estate in the early hours of Tuesday morning.
The teenager's father Martin van Breda, 54, his wife Theresa, 55, and older brother Rudi, 22, were killed. Her other brother Henri, 20, survived.
Last week, police spokesperson Tembinkosi Kinana said no arrests had been made and no one had been taken in for questioning.
He declined to disclose how the family was killed, or a possible motive.
The family on Sunday said Henri was "coping under the circumstances" and was undergoing counselling.
A private memorial would be held for Martin, Teresa and Rudi at the Dutch Reformed Church in Moreleta Park, Pretoria, on Thursday.
The family asked for privacy during the memorial.
"The family expresses its deep gratitude to the doctors and nurses at the Medi-Clinic Vergelegen for the love and care shown to Marli and thanks the SAPS [SA Police Service] for the way in which they are approaching the investigation.
The family also expresses their thanks and appreciation for all the messages of condolences from friends and associates of Martin, Theresa and Rudi in South Africa, Australia and elsewhere abroad."