The 15-year-old's body was discovered on Tuesday 1.6 miles from a holiday resort where the family had been staying.
Early on Saturday the teenager's family issued a statement asking the media to only rely on comments issued on their behalf by the Lucie Blackman Trust (LBT) charity.
The statement said: "The family of Nora Quoirin would like to clarify several comments that have been attributed to the family or to people claiming to act on behalf of the family.
"They wish it to be made absolutely clear that the only comments and statements relating to the disappearance, death, investigation and any other matters that are actually from the family are those released via Matthew Searle of the Lucie Blackman Trust."
It added: "Any other comments and views are those of the speaker and do not necessarily reflect the views of the immediate family or an accurate portrayal of the facts."
The statement was issued following reports suggesting Nora's parents were considering asking for a -second postmortem on Nora's body to be sure pathologists had not missed any evidence.
Malaysian police said following the first postmortem that Nora starved after her disappearance and there was no evidence of abduction or kidnapping "for the time being".
After meeting Malaysia's deputy prime minister on Friday, her family said they are "struggling to understand the events of the last 10 days".
"The initial postmortem results have given some information that helps us to understand Nora's cause of death.
"But our beautiful innocent girl died in extremely complex circumstances and we are hoping that soon we will have more answers to our many questions."
Malaysian police said Nora is likely to have spent a week in the jungle on her own.
The London teenager, who was born with the brain defect holoprosencephaly and was described by her family as "vulnerable", went missing from the resort of Dusun on Sunday August 4.
She died between two and four days before her body was discovered, a postmortem examination revealed.
The family said they will be bringing Nora's body home "where she will finally be laid to rest, close to her loving families in France and Ireland".
They also thanked Malaysian authorities and search parties for their efforts locating the teenager.
"Tragically, as we know, this wasn't enough to save Nora," they said.
Nora lived in London and was the daughter of French-Irish parents Sebastien and Meabh Quoirin.
The family attend St Bede's Catholic Church in Clapham, where a mass has been held for Nora this week.
Negeri Sembilan state police chief Mohamad Mat Yusop said on Thursday that the postmortem examination had found no evidence that the teenager had been abducted or raped.
He said she had died between two and four days previously, from intestinal bleeding, most likely due to starvation and stress.
He added: "The cause of death was upper gastrointestinal bleeding due to duodenal ulcer, complicated with perforation ... it could be due to a lack of food for a long period of time and due to prolonged stress."
He said there were some bruises on her legs but these would not have caused her death.
Further analysis is due on samples taken from her body, he added.
The trust said on Saturday that ongoing investigations would continue in France as is standard practice for overseas cases involving French citizens.
The LBT said it was arranging repatriation of Nora's body.
It also confirmed that no reward payments were made prior to the discovery of Nora's body, and noted that a police hotline remains open for those with information on the case.
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