Christians have taken to social media to share their thoughts and prayers for the Princess of Wales.
Kate said on Friday she was undergoing preventative chemotherapy after tests taken after she had major abdominal surgery in January revealed that cancer had been present.
The 42-year-old called the cancer discovery a "huge shock".
Kate spent two weeks in hospital in January after undergoing what her office said at the time was successful, planned surgery for an unspecified but non-cancerous condition.
However she said in a video message that subsequent tests had revealed cancer had been found. She said she was well and getting stronger.
"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," Kate said.
"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."
Following her operation, the palace had said the princess would not return to official duties until after Easter. But her absence from public life has provoked intense speculation and wild rumours on social media.
King Charles, 75, underwent a corrective procedure for an enlarged prostate at the same hospital as Kate in January. Buckingham Palace then revealed in February that he was to have treatment for cancer, meaning he has had to postpone his public royal duties.
"His majesty is ‘so proud of Catherine for her courage in speaking as she did'," a Buckingham Palace spokesperson said, saying Charles had been in close contact with Kate since they were at the private London Clinic together in January.
"Both their majesties ‘will continue to offer their love and support to the whole family through this difficult time’."
Prince Harry has also sent a message of support.
"We wish health and healing for Kate and the family, and hope they are able to do so privately and in peace," Harry and Meghan, the Duke and Duchess of Sussex, said.
Kensington Palace said it would give no further details about the type of cancer that had been found, saying the princess had a right to medical privacy. It said she was on a recovery pathway and the preventative chemotherapy had begun in February.
The timing of the announcement was to ensure that Prince George, 10, Princess Charlotte, 8, and Prince Louis, 5, had time to digest the news before it became public, and because Friday marked the start of their school holidays.
"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," Kate said.
"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 spirits."
Kate has not appeared at a public event since she joined other members of the royal family for a church service on Christmas Day.
However, a video filmed last Saturday by a member of the public which was published by the Sun newspaper showed Kate looking healthy, walking and carrying shopping bags alongside her husband at a farm shop in Windsor, near to their home.
"We hope that you will understand that, as a family, we now need some time, space and privacy while I complete my treatment," Kate said.
"My work has always brought me a deep sense of joy and I look forward to being back when I am able, but for now I must focus on making a full recovery."
Kensington Palace said William would continue his duties while supporting his wife, as he had since her surgery. A source said Kate was in good spirits and focused on her recovery.
However, neither will be present for the traditional gathering of royals for a church service on Easter Sunday at Windsor.
(Additional reporting by Reuters)
