Bonnie Tyler "remains seriously ill" but is stable following emergency intestinal surgery, a spokesman for the star has said.
The Welsh singer, 74, best known for Total Eclipse of the Heart, was put into an induced coma by her doctors to help her recovery.
She was rushed to a hospital near her home in Faro, Portugal, last week for the surgery.
On Tuesday, a spokesman for the singer said: "As of this morning, Bonnie remains seriously ill but stable in hospital in Faro. However, her doctors are still positive that she will make a full recovery."
He added that the family have been distressed by many "lurid and untrue rumours" circulating, adding that they ask for "privacy and decency at this difficult time".
The news of her surgery was revealed in an Instagram post on Wednesday last week.
Tyler, whose real name is Gaynor Hopkins, shot to fame in the 1980s after releasing her number one hit single Total Eclipse of the Heart.
The Grammy-nominated star went on to release a number of hit songs over the years, including Holding Out for a Hero and If You Were a Woman (And I Was a Man).
Tyler is due to tour Europe later this year to mark 50 years since the release of her 1976 breakthrough hit Lost in France, which entered the charts across Europe.
Source: Press Association
