King Charles III said Friday he is "so proud" of Catherine, Princess of Wales, for "her courage in speaking as she did", shortly after she revealed a cancer diagnosis in a video statement.
Charles, who is himself undergoing treatment for cancer, said he remains in the "closest contact with his beloved daughter-in-law", a spokesperson for Buckingham Palace said.
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.
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".
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.
Also watch: Harry and Meghan wish Kate 'health and healing'