The Holy See has “authorised the opening of an investigation”, the family's lawyer Laura Sgro told Italian media on Wednesday. The Vatican declined to comment.
Orlandi, the daughter of a member of the Vatican's police, was last seen leaving a music class aged 15, and theories have circulated for decades about who took her and where her body may lie.
The Vatican said last month that it may open a tomb within its grounds to see if it holds the girl's remains, after Sgro received an anonymous tip-off telling her to look inside the marble-topped grave.
According to some theories, the teenager was snatched by an organised crime gang to put pressure on Vatican officials to recover a loan.
Another claim was that she was taken to force the release from prison of Mehmet Ali Agca, the Turk who attempted to assassinate Pope Jean Paul II in 1981.
“After 35 years of a failure (on the part of the Vatican) to collaborate, the opening of an investigation is an important step,” Orlandi's brother Pietro was quoted by media as saying.
The family braced for a breakthrough in October when human remains were discovered on a Vatican property, only to be disappointed when tests showed the skeleton did not belong to a teenage girl.
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