"Our daughter, Allegra, has been battling anorexia, a very serious disease, for many years," Versace and Paul Beck said in a statement released Tuesday by spokesman Robert Zimmerman.
"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."
Versace, 51, first confirmed the news to syndicated entertainment show "The Insider" on Tuesday following recent media speculation and Internet chatter about her daughter's gaunt appearance.
Versace, the sister of the late designer Gianni Versace, and Beck are legally separated, Zimmerman said.