LONDON —King Charles III is frustrated by the length of time his recovery from cancer treatment is taking, his nephew has said, as Kate, the Princess of Wales, and Prince William thanked the public for their support after the revelation of her own diagnosis.

Peter Phillips, 46, the only son of Princess Anne and eldest grandchild of Queen Elizabeth II, said Sunday that his uncle, the king, was in “good spirits” following his shock diagnosis in February but was finding the recuperation period and his step back from public life a struggle.

“I think, ultimately, he’s hugely frustrated. He’s frustrated that he can’t get on and do everything that he wants to be able to do,” Phillips told Sky News Australia in an interview.

He continued: “But he is very pragmatic [and] he understands that there’s a period of time that he really needs to focus on himself.”

The news came as Kate and her husband William, the heir to the throne, said they were “enormously touched” by the outpouring of goodwill from around the world following her announcement on Friday that she was undergoing treatment for cancer.

“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,” said a spokesperson for Kensington Palace, which houses the couple’s official residence and private office.

“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,” the spokesperson added in a statement late Saturday.

The developments followed a tumultuous week for the British royal family, in which Kate ended weeks of speculation and conspiracy theories over her health with a rare video message. Many of those who posted jokes or wild speculation have since expressed their regret.

Kate, 42, was admitted to a private London hospital for major abdominal surgery in January. She said Friday that the unspecified surgery was successful but that subsequent tests showed that cancer was present.

Kensington Palace said she was receiving preventative chemotherapy, and Kate asked for privacy as the family — particularly the couple’s three young children — adjust to the news.

King Charles expressed his own support for his daughter-in-law on Friday and Buckingham Palace said the pair had become close through their shared hospital stays.

The king was “so proud of Catherine for her courage in speaking as she did,” a statement from the palace said, adding that he had “remained in the closest contact with his beloved daughter-in-law throughout the past weeks.”

The ill health of Kate and Charles has left the family short of frontline members to fulfil royal duties.

Peter Phillips, who is 18th in line to the throne, said in his interview that the king was trying to return to public life as much as he could during treatment.

“He is always pushing, his staff and everybody and his doctors and nurses to be able to say ‘actually come on, you know, can I do this? Can I do that?'” he said.