The bone fragments were unearthed during construction work at the Vatican’s embassy to Italy, in the Rome district of Parioli.
The Vatican announced on Tuesday that experts were trying to determine the age, sex and date of death of the remains.
A preliminary examination of pelvic bones confirmed that the remains belong to a female, according to Italian news agency ANSA.
Italian media have suggested the bones may be those of a 15-year-old girl who went missing in 1983.
Emanuela Orlandi – the daughter of a Holy See employee – was last seen on June 22, 1983, leaving her music lesson in Rome.
The teenager’s disappearance has been linked to organised crime or to an attempt to force the release from prison of Mehmet Ali Agca, the man who tried to assassinate Pope John Paul II in 1981.
Local media have also speculated the remains could belong to Mirella Gregori, who was also 15 years old when she vanished in the Italian capital, just 40 days before Orlandi.
On May 7, 1983, Gregori answered the intercom at her family’s apartment and told her parents it was a friend from school.
She said she was going out to speak to him, and was never seen again.
Detectives say it is possible that the two mysteries are connected.
Investigators are comparing the cranium and teeth with the DNA of Orlandi and Gregori, ANSA said.
A lawyer representing Orlandi’s family has demanded more details after the discovery of the remains.
“We will ask the Rome prosecutors’ office and the Holy See how the bones were found and why the discovery has been related to the disappearance of Emanuela Orlandi and Mirella Gregori,” Laura Sgrò said.
“The statement released yesterday by the Holy See does not provide much information.”
Gregori’s sister Maria Antonietta said she didn’t want to get her hopes up too soon that she may finally get closure.
“I don’t want to delude myself,” she told ANSA.
“I want to stay with my feet on the ground, but in my heart I hope that those bones belong to Mirella, so we can put an end to this affair and I would have a place to go to mourn and take a flower to my sister.”
