Kate Middleton, Prince William 'enormously touched' by well wishes ...

Kate Middleton and Prince William are both "enormously touched" by the well wishes from the public following the Princess of Wales' announcement that she was diagnosed with cancer, Kensington Palace 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," a palace spokesperson said in a statement Saturday. "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."

Kate revealed she was diagnosed with cancer and is undergoing chemotherapy in a video message released Friday. The type of cancer has not been disclosed. Kate started a course of preventative chemotherapy in late February, according to Kensington Palace.

"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," Kate, 42, said in the video, which was filmed at Windsor on Wednesday. "As you can imagine, this has taken time. It has taken me time to recover from major surgery in order to start my treatment."

The cancer was discovered in post-operative tests after her planned abdominal surgery in mid-January, she said.

"The surgery was successful," Kate said. "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."

At the time of Kate's surgery, Kensington Palace said her condition was non-cancerous. The palace has provided little information on her condition since.

Kate said having her husband at her side has been "a great source of comfort and reassurance."

"We hope that you will understand that, as a family, we now need some time, space and privacy while I complete my treatment," she said.

The Prince and Princess have three young children -- Prince George, 10, Princess Charlotte, 8, and Prince Louis, who will turn 6 in April.

Kate will return to official duties when she's cleared by her medical team, according to the palace.

The announcement sparked an outpouring of support and comes as Kate's father-in-law, King Charles III, also undergoes cancer treatment.

ABC News' Emily Shapiro and Katie Kindelan contributed to this report.