Nida Ul Naseer, 18, of Newport, south Wales, has not been seen since she stepped outside at her home in Linton Street on December 28.
The teenager suffers from a medical condition and needs medication without which she is likely to become anaemic.
A major police search operation to find her, which has gone on in extreme weather, is continuing.
Her father Naseer Tahir, sister Naila Anwar and a brother appeared together in an interview on ITV's Daybreak programme yesterday morning.
The programme said they felt that earlier reports of a family argument involving Nida had been taken out of context.
It also showed a printed sign pinned to the front door of their home in Newport which reads: "Nida please come home. Don't worry. We are all missing you."
Her father said: "We have some issues, but only in the family. The family are good. We want to see Nida here."
Naila Anwar described her sister as very close to her family, adding: "She would always share everything with us. It is just out of character".
She said of her sister: "She can't live without a phone. She just always talks to me on the phone."
She agreed there was no indication that her sister had in any way prepared to leave before vanishing. She had packed nothing.
"Everything is at home, her purse that she used, everything is at home, she's not even taken her coat. Nothing."
Nida is described as a quiet and very shy girl who is addicted to her mobile phone and afraid of the dark.
It is not known what condition she suffers, as it is understood that the family have declined to elaborate.
Her sister added: "If you know anything about Nida, just tell us, just call the police. We just want to know that she's safe."