The Vatican is under pressure to help resolve one of the strangest of many enigmas lingering in Italy from the cold war years.

For four years, prosecutors in Rome have been making a renewed attempt to get at the truth behind the disappearance in 1983 of Emanuela Orlandi, the 15-year-old daughter of a Vatican employee.

They are seeking to ascertain whether she was seized by a notorious band of Rome criminals, and whether this has any bearing on the fact that the leader of the gang was buried in a Vatican basilica normally reserved for cardinals and other illustrious prelates.

Last month, Walter Veltroni, a former deputy prime minister, asked the interior minister in Mario Monti's government to confirm that the basilica of Sant'Apollinare, a few yards from the Piazza Navona in central Rome, did not enjoy extra-territorial status and was thus subject to Italian law.

His question was interpreted as an attempt to clear the way for the prosecutors to order the reopening of the tomb in which gangster Enrico de Pedis has been interred since 1990.

Emanuela's body has never been found and, according to one of the many theories about her disappearance, it was laid to rest alongside that of De Pedis. But at the beginning of the month, prosecutors unexpectedly withdrew support for the exhumation while briefing Italian reporters that they believed at least one high-ranking Roman Catholic cleric had information about her disappearance.

A source close to the prosecution service was quoted as saying "behind the sacred walls, someone is still alive [and] in possession of evidential fragments of the truth". But in an interview with the daily Corriere della Sera, Cardinal Giovanni Battista Re said: "If anyone on the inside had known anything, he would have said it. We were all interested in clearing [the case] up."

Her brother, Pietro Orlandi, expressed astonishment at the prosecutors' decision not to open De Pedis's tomb. "I don't understand what could have made them change their minds," he said.

According to a report in the Rome daily La Repubblica, the prosecutor leading the inquiry has visited the crypt where the gangster is buried under a marble structure copied from the tomb of a pope.

Conspiracy theorists have linked Emanuela's disappearance at a bus stop to any number of other events. She vanished as investigators were looking into the still obscure reasons for the assassination attempt on Pope John Paul II, and the murky affairs of the Vatican bank after the mysterious death in London of the financier Roberto Calvi.

In 2005, attempts to solve the case were given new life when an anonymous caller rang an Italian television programme to allege that Emanuela had been kidnapped as a favour to the man who was in 1983 the vicar general of Rome, Cardinal Ugo Poletti, and that whoever sought to solve the riddle should see who was buried in the basilica of Sant'Apollinare.

Subsequently De Pedis's former lover gave prosecutors another explanation: that Emanuela had been kidnapped and murdered by the gang on the orders of Archbishop Paul Marcinkus, at that time the president of the Vatican Bank. Marcinkus died in 2006.

Last year, a former gang member offered a third version, saying the teenager had been seized and held hostage in an effort to get back money invested by its members through the Vatican bank.

Antonio Mancini said that De Pedis decided to write off the money and stop pressuring the Vatican, and claimed this was how the gangster earned his interment in one of Rome's most august places of worship.

De Pedis – nicknamed Renatino – was shot dead in an ambush in a cobbled street near the Campo de' Fiori in 1990. The moving of his body from a cemetery to the basilica of Sant'Apollinare only came to light seven years later because of investigations by a journalist.

It subsequently emerged that the move was authorised – in apparent violation of canon law – by Cardinal Poletti.

The rector of the basilica at the time, Piero Vergari, later wrote: "I never knew anything about [De Pedis's] relations with other people … He helped me a lot to prepare the soup kitchens I organised for the poor."