The Welsh singer, 74, known for Total Eclipse of the Heart, was put into an induced coma by her doctors to help her recovery after being rushed to a hospital near her home in Faro, Portugal, for the procedure.
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 said the family had been distressed by many "lurid and untrue rumours" circulating, adding they asked for "privacy and decency at this difficult time".
The news of her surgery was revealed in an Instagram post on May 6.
Tyler, whose real name is Gaynor Hopkins, shot to fame in the 1980s after releasing her number one UK 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, It's a Heartache and If You Were a Woman (And I Was a Man).
Tyler is due to tour Europe later in 2026 to mark 50 years since the release of her 1976 breakthrough hit Lost In France, which entered the charts across Europe, with performances scheduled in May in Malta and Germany.
Her upcoming tour also includes shows across the UK, as well as in Austria, Hungary, Turkey and Romania.
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