Kate and William 'extremely moved' by support since the Princess of Wales' cancer revelation

Kate, the Princess of Wales, and her husband, Prince William, are said to be "extremely moved" by the public's warmth and support following her shocking cancer announcement as tributes continued to pour in from around the world.

After weeks of frenzied speculation on social media about her health and well-being, Kate said in a candid video message on Friday that she is undergoing chemotherapy for cancer following major abdominal surgery. The 42-year-old princess said the cancer discovery was a "huge shock" and she was now in the early stages of preventative chemotherapy.

"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 spokesperson for Kensington Palace said. "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."

There has been a global outpouring of support, including from U.S. President Joe Biden, and King Charles III who is also undergoing treatment for cancer, which was found after he was undertaking treatment for an enlarged prostate. Neither Kate nor the king have revealed what type of cancer they have or the stage at which it was being treated.

Charles' nephew, Peter Phillips, said the king is "frustrated" that his recovery is taking longer than "he would want it to," but that he was in "good spirits" and "pushing" his staff to be able to return to his duties after beginning his treatment for cancer last month.

"I think ultimately he's hugely frustrated," Phillips, the son of Charles's sister Princess Anne, told Sky News Australia. "He's frustrated that he can't get on and do everything that he wants to be able to do. But he is very pragmatic, he understands that there's a period of time that he really needs to focus on himself."

People continued to flock Sunday to the royal's main London residence, Kensington Palace, as well as to Windsor Castle, where they spend most of their time, to show support for the princess, with many leaving flowers.

Until Friday, officials had only said Kate's surgery in January was successful and recuperation would keep the princess away from public duties until April. This has sparked a flurry of rumor-mongering about the "missing" future queen, compounded after Kate acknowledged that she altered an official photo released to mark Mother's Day in the U.K. earlier this month.

The photo, meant to reassure the public, triggered a backlash after The Associated Press and other news agencies retracted it over manipulation concerns.

Even a video published last week by The Sun and TMZ that appeared to show Kate and William shopping near their home didn't dispel the negative coverage.

Criticism of those jumping to sometime-outlandish conclusions continued to be voiced over the weekend.

Paddy Harverson, previously the official spokesman of Kate and the Prince of Wales, said that the speculation and pressure around Kate's health and whereabouts before her video statement was "the worst I've ever seen."

However, he said he thought Kate would have revealed her cancer diagnosis exactly as she had, regardless of what was being speculated.

"I'm absolutely convinced that if we hadn't had all the madness and social media, if we hadn't had the sort of the Mother's Day photo mistake, they would have still done it like this," he told the BBC. "They would have still waited till this last Friday when the schools are breaking up to make the announcement."