Image source, ReutersFormer royal spokesman Paddy Harverson has urged the public to give the Prince and Princess of Wales "time to heal" after Catherine's cancer diagnosis.
Mr Harverson said King Charles, who is also receiving treatment for cancer, was "very resilient".
Once the Royal Family is "through this sticky patch, I think we'll get back to normal", he added.
Catherine revealed on Friday that she had begun treatment, after weeks of speculation about her condition.
She said cancer was discovered after she underwent abdominal surgery.
Details of the cancer have not been disclosed, but Kensington Palace says it is confident the princess will make a full recovery.
That news comes six weeks after King Charles paused his public appearances following a cancer diagnosis himself.
The two were briefly treated at the London Clinic private hospital at the same time.
Speaking to the BBC's Sunday With Laura Kuenssberg programme, Mr Harverson – a former official spokesperson for William and Catherine – said he did not believe the Royal Family was "more fragile because of recent illnesses".
Asked about how Kensington Palace has handled the situation, he said: "This is not just an institution, it is a family and you have to deal with the individuals and the members of the family as you would anyone else," he said.
"You have to give them the space so while there might be communications… you also have to remember they are human beings and you have to follow their lead to a certain degree," he added.
The couple have faced intense public speculation about Catherine's health, since her operation in January for a condition that had not been revealed.
Catherine, 42, has not attended any official events since Christmas.
A photograph of her and her children, released on Mothers' Day, was met with a frenzy on social media due to inconsistences in the picture.
In a statement, Catherine later apologised for "any confusion" caused by the photo, and said that "like many amateur photographers, I do occasionally experiment with editing".
Mr Harverson said he had "no issue" with how the Royal Family had dealt with the announcement of Kate's diagnosis, and criticised the "permanent death loop" of speculation on social media.
"I am sure she wanted the picture to be as best as possible and she apologised for it so everyone should have moved on," he said. "I really do think we should give them time and space".
"They will get over this," he added. "I am highly confident that the King, who I know well, is incredibly strong, very resilient, a great spiritual person."
A Kensington Palace spokesman has said the Prince and Princess of Wales were "enormously touched by the kind messages" they have received, and that they were "grateful for the understanding of their request for privacy at this time."
The couple have already said they will not attend this year's Easter Sunday service. It is unclear if King Charles will lead his family to church.
Buckingham Palace say they are "hopeful" he will be able to join the family next weekend.
The King has said he is "so proud" of his "beloved daughter-in-law" and that he and Camilla are in the "closest contact" with her.
The BBC understands that the Duke and Duchess of Sussex have reached out to William and Catherine since her diagnosis.
You can watch a BBC News special programme about how the Princess of Wales revealed her cancer diagnosis in a video message to the nation – 'Kate's Cancer diagnosis' – on BBC iPlayer, now.