Johnny Depp's 7-year-old daughter, who has reportedly been receiving treatment in a British hospital, is "much better," the star's publicist said Thursday.

Britain's Daily Mirror newspaper reported that Lily-Rose, daughter of Depp and French singer Vanessa Paradis, was admitted to a hospital nine days ago and was in a serious condition.

The newspaper said Thursday it knew the location of the hospital and the nature of the child's ailment, but wasn't revealing details to preserve the family's privacy.

"We are happy to report that their daughter is doing much better," said Depp's publicist, Robin Baum. "The family greatly appreciates the continued support and respect of their privacy."

Lily-Rose has blood poisoning contracted from stepping on a rusty nail, according to In Touch magazine.

"After the wound was left untreated, blood poisoning developed. It has now spread through her body and has affected her vital organs," an insider told the magazine.

Depp, 43, is in Britain to film "Sweeney Todd," director Tim Burton's musical about the legendary "demon barber of Fleet Street."

Depp and Paradis also have a 4-year-old son, Jack.