Kate, as she is widely known, said the discovery of cancer, after successful abdominal surgery in January, was "a huge shock" but she was "well and getting stronger every day"
Kate was last seen at a public engagement on December 25, when she joined the king and other senior royals at a Christmas Day church service.
Catherine, Princess of Wales, on Friday announced that she has cancer and is in the early stages of chemotherapy, asking for "time, space and privacy" as she completes her treatment.
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Kate, as she is widely known, said the discovery of cancer, after successful abdominal surgery in January, was "a huge shock" but she was "well and getting stronger every day".
The disclosure came after royal officials said in February that King Charles III was being treated for cancer, forcing him to cancel all public engagements.
Charles said he was "so proud of Catherine for her courage in speaking as she did", leading messages of support, including from UK Prime Minister Rishi Sunak and the White House.
Kate's brother James Middleton, posted a photograph of himself with his sister as children on Instagram, commenting: "Over the years, we have climbed many mountains together.
"As a family, we will climb this one with you too."
William's estranged US-based brother Prince Harry and his wife Meghan Markle said they wished "health and healing for Kate and the family".
'Preventative' chemo
Like Charles, the 42-year-old princess, whose husband Prince William is heir to the throne, did not disclose the exact nature of the cancer.
But she described the months since she went into hospital as "incredibly tough" for her, William and their three young children.
"In January, I underwent major abdominal surgery in London and at the time, it was thought that my condition was non-cancerous," she added in a video statement, filmed on Wednesday at Windsor, west of London, where they live.
"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."
Preventative chemotherapy is given "after an operation to prevent recurrence", said Shivan Sivakumar, associate professor in oncology at the University of Birmingham in central England.
"This is to attempt to destroy any circulating cancer cells," he added.
Kate -- one of the most photographed women in the world -- is a central figure in the royal family and married Prince William, 41, in 2011.
She said it had taken them time to explain the situation to Prince George, aged 10, Princess Charlotte, eight, and five-year-old Prince Louis, "and to reassure them that I am going to be OK".
William, Kate and their children are seen as the modern face of the British royal family, and key to its future as it faces declining support, particularly among younger people.
Palace officials will be hoping that the unusually candid disclosure will end speculation and rumours about her health and whereabouts, particularly online.
'Open'
"I think it's important to know that they're human just like us," Hannah Dickerson, visiting London from the United States, told AFP outside Buckingham Palace.
"I think it's very, very good that they're open about showing that they're not afraid to hide it."
Kate was last seen at a public engagement on December 25, when she joined the king and other senior royals at a Christmas Day church service.
Kensington Palace announced on January 17 that she was facing up to two weeks in hospital and several months' recuperation following abdominal surgery.
She was not expected to be ready to return to public duties until after Easter on March 31, a statement at the time said.
Royal officials did not disclose the exact nature of her condition but said it was not cancer-related.
That announcement came shortly before a separate statement from Buckingham Palace that 75-year-old Charles was to have surgery for a benign enlarged prostate.
Photo controversy
He later spent three days at the same private hospital in central London. Officials then said in early February that tests had identified "a form of cancer", without giving further details.
The king has cancelled all public engagements except audiences with the prime minister and ambassadors, and worked on official papers while undergoing treatment.
He has been photographed several times since then, and been seen attending church.
Kensington Palace sought to end mounting questions about Kate, releasing a Mother's Day photograph said to have been taken by William.
But the plan backfired after it was later found to have been digitally altered and saw leading news agencies, including AFP, pull the image.
British media this week published new images of the princess walking with William at a farmers' market near their Windsor home.
This week, there were claims that an attempt may have been made to access Kate's confidential medical records, prompting a referral to the UK data protection watchdog.
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