The 20-year-old heiress of the Versace fashion house has been suffering from anorexia for a number of years but is in a stable condition, her parents said on Wednesday.
In a joint statement intended to quell speculation about their daughter's health, designer Donatella Versace and her ex-husband, Paul Beck, said Allegra had "been battling anorexia, a very serious disease, for many years".
"She is receiving the best medical care possible to help overcome this illness and is responding well," said the statement.
"Allegra is not at present staying in any hospital, she is living in her private residence and her condition does not cause particular concerns," it said.
"As parents, we are doing our best to protect our daughter," the statement continued. "However, due to numerous media reports, we want to let everyone know that we appreciate their concern for Allegra, and we ask that her privacy be respected at this time".
Wednesday's statement, the second in two days, was issued in response to a fresh series of media reports that have appeared over the last few hours.
Several of these included statements allegedly by Donatella, which lawyers for the fashion house claim are fabricated.
The firm's legal office has said it plans to sue Italy's largest daily, Corriere della Sera, for an article published on Wednesday, which allegedly contained untrue comments attributed to Donatella.
Two weeks ago, Allegra's family started legal proceedings against an Australian daily, after it reported she was close to death in hospital.
The 20 year old's precise location is unknown, but she is thought to be staying at a Versace property in New York, not far from Rhode Island where she is studying acting and marketing at Brown University.
A spokesperson for the fashion house in Italy said Allegra had been "ill for 10 years but she is now getting better".
Allegra inherited 50% of the fashion house on her 18th birthday from her uncle, Gianni Versace, who was murdered in 1997.
The Versace founder, who reportedly adored Allegra, was gunned down in Miami by serial killer Andrew Cunanan.
The speculation about the Versace heir comes not long after heated debate over links between the fashion world and anorexia.
In the last year, two models have died from anorexia-related complications, Luisel Ramos of Uruguay and Ana Carolina Reston of Brazil.
The deaths have prompted action in the fashion world in a number of countries. Spain has banned overly skinny models from the catwalks, while a number of Italian stylists have signed a code of conduct, agreeing not to use under-age models and requiring medical certification before they appear in shows.
