Kate and William were “deeply affected” by the public support

A Kensington Palace spokesman said the Prince and Princess of Wales were “deeply touched by the kind messages” they received after Catherine was diagnosed with cancer.

Saturday's statement also added that they were “grateful” that the public understood their request for privacy.

Katherine revealed in a video message on Friday that she had begun treatment.

She received her diagnosis after tests following abdominal surgery “found the presence of cancer”.

A Kensington Palace spokesman said: “The Prince and Princess have been hugely touched by the kind messages from people here in the UK, across the Commonwealth and around the world in response to Her Royal Highness’s letter.

“They have been extremely touched by the public’s warmth and support and are grateful that their request for privacy is understood at this time.”

This statement is the last we will hear from the Prince and Princess for a while.

It's both a thank you note and a polite warning – the couple saying the public aspect of this diagnosis is over and they want to be left alone.

It is also an acknowledgment of the overwhelmingly positive response to Katherine's video message.

Social media has been a toxic place for the princess in recent weeks due to wild rumors and gossip about her condition.

At the time of writing, Katherine's video message, posted on Instagram, had been liked nearly five million times.

Their final statement of thanks is the final chapter in this stage of the Princess's diagnosis, and Kensington Palace wants to put an end to all this speculation.

The past few weeks have been difficult for the royal couple, their children and the team around them who have been trying to quell gossip and rumors – a task that has proven impossible.

The statement acknowledges the global interest in the princess's condition, with references to the UK, the Commonwealth and the world.

But the last few words are perhaps the most important – a direct plea for privacy while trying to escape the glare.

Prince George, Princess Charlotte and Prince Louis began their Easter school holidays on Friday.

They will not return to school until April 17, and we do not expect to see or hear from the family during the break.

They have made it very clear that this is family time that they will fiercely protect.

The central element of any royal Easter is the church service on Easter Sunday, which is usually a powerful gathering of royals at St. George's Chapel in Windsor.

Prince William and Catherine have already said they will not attend Mass this year, but we may see King Charles III leading the family to church.

Buckingham Palace says they are “hopeful” he will be able to join the family next weekend.

The king said he was “very proud” of his “beloved daughter-in-law” and that he and Camilla were in “the closest contact” with her.

Almost all Sunday newspapers begin with a reaction to the news of the Princess of Wales's cancer diagnosis.

The Sunday Express wrote of a “nation moved” by Catherine's courage and dignity while the Daily Star Sunday noted some speculation about her health ahead of the announcement, saying celebrities had “now rushed to apologise”.

Royal commentator Paddy Harverson, who was previously William and Catherine's official spokesman, told the BBC that he did not believe the institution of the royal family had become any more “fragile” due to recent illnesses.

He told the BBC's Sunday with Laura Kuenssberg programme: “We just have to come to terms with the new reality, there are fewer of them.

“And so everyone just needs to understand that they're going to keep busy, and they're going to get through this. I'm very confident that the King, who I know very well, is incredibly strong, very resilient, and a great spiritual person, so I know he'll get through this.”

“Likewise, with the princess, with Kate, I think once we get through this sticky patch, I think we'll go back to normal.”

You can Watch a BBC News special programme On how the Princess of Wales revealed her cancer diagnosis in a video message to the nation – 'Kate's Cancer Diagnosis' – on BBC iPlayer now.