The 42-year-old royal went under the knife on January 16, but online speculation on her whereabouts has recently increased, leading the royals to speak out again.
A royal spokesperson told the New York Post newspaper's Page Six column: "Kensington Palace made it clear in January the time-lines of the princess’ recovery and we’d only be providing significant updates.
"That guidance stands." They also reiterated that Catherine is "doing well". The princess is expected to return to royal engagements after Easter.
It was recently claimed Catherine has been spending time with her family - husband Prince William, and children Prince George, 10, Princess Charlotte, eight, and Prince Louis, five - since she came home from hospital, and another insider recently suggested she's making good progress, too.
The source told the Daily Mail newspaper's Richard Eden: "Catherine is recovering well. She was looking forward to a change of scene and will be able to take it easy in Norfolk while the children let off steam with William."
The princess' operation was described as "successful", and the palace previously confirmed she's unlikely to return to public duties until after Easter.
The palace said in a statement on January 17: "The surgery was successful and it is expected that she will remain in hospital for 10 to 14 days, before returning home to continue her recovery.
"Based on the current medical advice, she is unlikely to return to public duties until after Easter."
Earlier this week, William pulled out of a memorial service for undisclosed "personal reasons".
The 41-year-old royal was scheduled to attend a memorial service for King Constantine of Greece - who died in January 2023, aged 82 - at Windsor Castle on Tuesday, but he withdrew from the event.