Donatella and Allegra Versace in November 2006
03/28/2007 at 08:00 AM EDT
Allegra Versace, the 20-year-old daughter of fashion designer Donatella Versace and niece of the late Gianni Versace, is in treatment for anorexia, her mother confirmed Tuesday.
"Our daughter, Allegra, has been battling anorexia, a very serious disease, for many years," Donatella Versace and Allegra's father, estranged husband Paul Beck, said in a statement released by spokesman Robert Zimmerman, the Associated Press reports.
"She is receiving the best medical care possible to help overcome this illness and is responding well. As parents, we are doing our best to protect our daughter. 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," the statement reads.
Versace, 51, first confirmed the news to TV's The Insider
on Tuesday after continued speculation about her daughter’s increasingly skeletal appearance.
Versace, the sister of the late designer Gianni Versace, spent yesterday launching her new signature fragrance, Versace, in London at the upscale department store Harrods. When asked by PEOPLE how Allegra was faring, Versace – who was en route home to Milan – declined to comment.