The unclothed body of 15-year-old Nora Quoirin was discovered in August after a massive hunt through dense rainforest not far from the resort where the London-based family had been on holiday.
Her parents say they believe there was a "criminal element" to her death as the teen had learning difficulties and would not have wandered off alone, but Malaysian police insisted there was no sign of foul play.
The girl disappeared a day after arriving at the Dusun Resort, triggering a 10-day hunt involving hundreds of people, helicopters and sniffer dogs.
Her body was found more than a mile from the resort.
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An autopsy found Nora likely starved and died of internal bleeding after about a week in the jungle, police said in August, adding there was no indication she was abducted or sexually assaulted.
But her parents have challenged the findings and are pushing for an inquest after Malaysian authorities classified the teenager's case as "requiring no further action", effectively closing it unless new evidence emerged.
The family's lawyer in Malaysia, Sankara Nair, told AFP on Wednesday that he has written a letter to the Attorney-General, Tommy Thomas, calling for an inquest.
"We want to determine the circumstances that led to her death," he said.
"In the letter I told the Attorney-General that we suspect there is a case of criminal element, i.e. an abduction, as there are many questions raised by us and the family that have remained unanswered by the police."
Nora's parents, Meabh and Sebastian Quoirin, issued a statement at the weekend from London saying they were informed the case had effectively been closed.
"We are shocked by this decision," they said, adding it "prevents justice being done".
The family has also filed a civil suit against the resort, seeking at least 182,000 ringgit ($45,000) in damages.
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