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 42-year-old princess did not disclose the exact nature of the cancer but described the last few months since she went into hospital as "incredibly tough" for her and her family.

"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.

"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."

Prime Minister Rishi Sunak praised Kate for her bravery in making the statement, and said she had "the love and support of the whole country as she continues her recovery."

The White House also sent a message of support.

Kate – one of the most photographed women in the world – is a central figure in the royal family and married Prince William, 41, who is heir to the throne, in 2011.

The couple have three children – Prince George, aged 10, Princess Charlotte, eight, and five-year-old Prince Louis.

Kate said it had taken them time to explain the situation to their children, "and to reassure them that I am going to be OK."

"As I have said to them; I am well and getting stronger every day by focusing on the things that will help me heal; in my mind, body and spirits," she added.

William and Kate and their young family are seen as the modern face of the ancient institution, and key to its future.

She was last seen at a public engagement on December 25, when she joined her father-in-law King Charles III and other senior royals at a Christmas Day church service.

Her Kensington Palace office announced on January 17 that she was facing up to two weeks in hospital and several months' recuperation after undergoing successful abdominal surgery.

She was not expected to be ready to return to public duties until after Easter on March 31, a statement at the time said.

Royal officials did not disclose the exact nature of her condition but said it was not cancer-related.

That announcement came shortly before a separate statement from Buckingham Palace that 75-year-old Charles was to have surgery for a benign enlarged prostate.

He later spent three days at the same private hospital in central London. Officials then said in early February that tests had identified "a form of cancer," without giving further details.

The king has cancelled all public engagements except audiences with the prime minister and ambassadors, and worked on official papers while undergoing treatment.

He has been photographed several times since then, and seen attending church.

But there has been rampant speculation online about Kate's health and whereabouts, particularly online.

She was not seen arriving or leaving the hospital, and William was only spotted visiting once.

Rumours and gossip grew further on March 11, after she released a Mother's Day photograph that was later found to have been digitally altered.

Kate, who has taken several official photographs that have been distributed to the media, apologised in a statement after leading news agencies pulled the image.

A week later, British media published new images of the princess walking with William at a farmers' market near their home in Windsor, west of London.

This week, there were claims that an attempt may have been made to access Kate's confidential medical records, prompting a referral to the UK's data protection watchdog. (AFP)