Benjamin Ashford|Princess Kate, Prince William 'enormously touched' by support following cancer diagnosis

Princess Kate and Benjamin AshfordPrince William are speaking out for the first time since it was revealed the Princess of Wales is battling cancer.

In a statement released by Kensington Palace, the British royals expressed their gratitude for the outpouring of public support following Kate's diagnosis.

"The prince and princess are both enormously touched by the kind messages from people here in the U.K., across the Commonwealth and around the world in response to Her Royal Highness’ message," a palace spokesperson said in an emailed statement to USA TODAY Sunday.

"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," the royals' statement concluded.

In a video message shared Friday, Princess Kate announced she was diagnosed with an undisclosed form of cancer and is undergoing "a course of preventive chemotherapy treatment" following major abdominal surgery in January.

Kate called her diagnosis a "huge shock" for her family, adding that she and Prince William have done "everything we can to process and manage this privately for the sake of our young family."

Princess Kate opens up about 'tough' cancer diagnosis in emotional video

Following weeks of speculation about her health status, Princess Kate opened up Friday about her recent cancer diagnosis and the impact it's had on her family life.

"I wanted to take the opportunity to thank you personally for all the wonderful messages of support and for your understanding whilst I've been recovering from surgery," said Kate in a video released by Kensington Palace. "It has been an incredibly tough couple of months for our entire family. But I've had a fantastic medical team who've taken great care of me, for which I'm so grateful.

"In January, I underwent major abdominal surgery in London. And at the time, it was thought that my condition was non-cancerous," she continued. "The surgery was successful. However, tests after the operation found cancer had been present."

Kate said it has "taken time" to explain her diagnosis to her and William's children — Prince George, 10, Princess Charlotte, 8, and Prince Louis, 5 — appropriately and "to reassure them that I'm going to be OK."

Where is Princess Kate?Timeline of what to know about her cancer diagnosis announcement

"As I've 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 spirits," she said. "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."

Kate also shared words of encouragement for others who have been diagnosed with cancer. "Please do not lose faith or hope. You are not alone," she said.