"Thankfully, this has been caught early and now everyone will be wishing him that he gets the treatment that that he needs and makes a full recovery," Sunak said in what appeared to be off-the-cuff remarks during a radio interview with the BBC.
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Sunak said he was "like everyone else ... shocked and sad" at the news.
Buckingham Palace announced Monday that Charles, 75, had been diagnosed with an undisclosed form of cancer after being admitted London hospital for a corrective procedure for an enlarged prostate last month. A royal source told CNN that the form of cancer detected was not prostate cancer, but did not specify further.
Charles will step back from public-facing duties while he undergoes treatment, the palace said. He will continue to carry out state business and official paperwork.
That means he's likely to carry on getting his daily red boxes with government papers so he can continue working through state documents at home. CNN understands that it is anticipated the king will continue his weekly audience with the prime minister and that alternative arrangements will be made if his doctors advise him to minimize in-person contact.
It is also understood that he will continue to be available for state duties like Privy Council meetings. However, details of how that will occur are still being worked out.
Sunak said he is still in regular contact with the king and will continue to communicate with him as normal. Sunak declined to say whether their face-to-face meetings would continue but hinted that the diagnosis would not affect how the country is run.
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"We'll crack on with everything, but he'll be in our thoughts and our prayers," Sunak said.
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Though all the signals coming from the palace have been positive so far, the news is disconcerting. It has been only about 17 months since Charles acceded to the throne following the death of his mother Queen Elizabeth II. She reigned for more than 70 years, longer than any British monarch in history.
Prince William, Charles' son and the heir to the throne, and Queen Camilla are expected to take on more public engagement to account for Charles' absence.
William had taken time off to support his family after his wife Catherine had surgery last month. It is unclear what her surgery was for, but a royal source told CNN last month that the 42-year-old's condition was non-cancerous.
William is in regular contact with his father, according to a source close to the Prince of Wales.
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Other working members of the family are continuing their public engagements and CNN understands they could also pick up some additional duties on Charles' behalf if needed. However, the number of public-facing "working royals" - those carry out engagements on behalf of the King - has dwindled in recent years.
That group consists of 11 members, more than half of whom are over the age of 70. It includes King Charles, Queen Camilla, Princess Anne, the Duke and Duchess of Edinburgh, the Waleses, the Duke and Duchess of Gloucester, and the Duke and Duchess of Kent.
Prince Harry and Meghan, Duchess of Sussex would normally be considered working royals, but they chose to step back from royal duties in 2020 and move to California. Prince Andrew was forced out in the light of his relationship with the late pedophile Jeffrey Epstein.
Harry, who has spoken with his father since his cancer diagnosis, returned to the United Kingdom Tuesday, British media reported. The duke flew from California to see the king, who it is thought he hadn't seen since the coronation in May.
The king's younger son was photographed being driven into Clarence House, near Buckingham Palace, Tuesday.
The Associated Press contributed to this report.
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