The Vatican City has agreed to open a pair of centuries-old tombs as part of the search for a 15-year-old girl who mysteriously vanished 36 years ago.

Relatives of Emanuela Orlandi, the daughter of a Holy See clerk, had asked for the graves in the tiny Teutonic Cemetery be unsealed following an anonymous tip that her remains could be hidden there.

The teenager, herself a Vatican citizen, went missing in 1983 after heading to a flute lesson in Rome.

Her disappearance is one of modern Italy’s most enduring mysteries, and drew renewed attention last year after Emanuela’s family received an anonymous letter suggesting her remains were buried in the cemetery for German nationals.

The letter referred to a marble statue of an angel above a tomb. It said: “Look where the angel is pointing."

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The two graves will be opened on 11 July with the teenager’s relatives and lawyers for the family and the Holy See present. The family had long urged the Vatican to look into Emanuela’s disappearance and reveal all official documentation about the case.

Vatican spokesman Alessandro Gisotti said the Holy See had opened an investigation after the teenager’s family "signalled the possible burial of her body in the tiny cemetery located inside Vatican State territory”.

Relatives of the people buried in the tombs will also be in attendance when they are opened, added Mr Gisotti, who did not identify the pair.

The exhumed bodies will be scientifically analysed to date them, and DNA testing will be carried out to see if any of the remains belong to Emanuela.

"After 35 years of lack of cooperation, the start of an investigation is an important breakthrough," Emanuela's brother, Pietro Orlandi, told Italian news agency Ansa.

Speculation about the teenager's fate has swirled in the Italian media since her disappearance.

Unproven theories put forward in the subsequent decades have suggested an attempt to secure the freedom of a gunman jailed for trying to assassinate Pope John Paul II and a connection to the grave of Enrico De Pedis, a mafia gangster buried in a Rome basilica. The mobster's tomb was opened in 2012 but nothing was revealed.

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Police at the time of Emanuela's disappearance did not rule out that she may have been abducted and killed for reasons with no connection to the Vatican or may have been a victim of human sex trafficking. She would be 51 today if still alive.