Princess Kate and Prince William are "enormously touched" by the public support following the mother-of-three's cancer diagnosis.
The Princess of Wales announced on Friday evening that she was undergoing a course of preventative chemotherapy for cancer.
This came as Kate, 42, was recuperating in private following her major abdominal surgery in January.
The royal was hospitalised for 13 days in The London Clinic, before returning home to Adelaide Cottage for her convalescence.
Prince William and Princess Kate issue new statement
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At the time, Kensington Palace said Kate's condition was noncancerous, however, tests following the operation showed that cancer was present.
The 42-year-old sat down in her garden at Adelaide Cottage to film a short video for the public, where she announced her cancer diagnosis to the world.
This video was released on Friday, following weeks of speculation and conspiracy theories online regarding Kate's whereabouts.
The Princess of Wales has received an outpouring of support from royal fans, commentators, politicians and leaders from around the world.
Kate announced via video message her cancer diagnosisPAOn Saturday evening, a Kensington Palace spokesperson issued a new statement on behalf of Prince William and Princess Kate.
They said: “The Prince and Princess are both enormously touched by the kind messages from people here in the UK, across the Commonwealth and around the world in response to Her Royal Highness’ message.
"They are extremely moved by the public’s warmth and support and are grateful for the understanding of their request for privacy at this time.”
During Kate's video address on Friday, she said: "I wanted to take this opportunity to say thank you, personally, for all the wonderful messages of support and for your understanding whilst I have been recovering from surgery.
Kate reiterated she is 'well' in her cancer announcementGetty"It has been an incredibly tough couple of months for our entire family, but I’ve had a fantastic medical team who have taken great care of me, for which I am so grateful.
"In January, I underwent major abdominal surgery in London and at the time, it was thought that my condition was non-cancerous. The surgery was successful. However, tests after the operation found cancer had been present.
"My medical team therefore advised that I should undergo a course of preventative chemotherapy and I am now in the early stages of that treatment."
The Princess of Wales continued: "This of course came as a huge shock, and William and I have been doing everything we can to process and manage this privately for the sake of our young family.
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Kate is recuperating in private at Adelaide CottageGetty"As you can imagine, this has taken time. It has taken me time to recover from major surgery in order to start my treatment.
"But, most importantly, it has taken us time to explain everything to George, Charlotte and Louis in a way that is appropriate for them, and to reassure them that I am going to be ok.
"As I have said to them; I am well and getting stronger every day by focusing on the things that will help me heal; in my mind, body and spirit.
"Having William by my side is a great source of comfort and reassurance too. As is the love, support and kindness that has been shown by so many of you. It means so much to us both."