Rishi Sunak's statement to the BBC states that King Charles III's illness was "caught early," and regular correspondence between the King and No-10 remains ongoing.
The prime minister expressed his profound dismay and sorrow upon receiving the news but assured that he would maintain frequent communication with the King.
The 75-year-old King has deferred his public responsibilities and started "routine therapies" for his ailment on Monday.
The Palace has officially announced that he is not suffering from prostate cancer. However, little more information has been provided.
During an interview with BBC Radio 5 Live, Mr Sunak expressed his condolences and said that the individual in question would be remembered and prayed for. He acknowledged that many families nationwide have experienced similar situations and understand the significance of such events.
The King's weekly meetings with Mr Sunak will continue in person unless medical professionals advise him to reduce such interactions.
The Palace has emphasised that the King would continue in his constitutional duty as the chief representative of the state, which entails finalizing administrative documents and conducting confidential discussions.
The Palace said on Monday that the King is "completely optimistic" about his recovery and eagerly anticipates resuming his regular activities.
After residing at Sandringham, the King travelled to London for outpatient cancer treatment. The day before, he was seen greeting the public by waving during a brief 10-minute stroll to the church.
The Prince of Wales, scheduled to resume his public duties this week after the Princess of Wales had abdominal surgery last month, is anticipated to take over some of his father's responsibilities while the King gets medical attention.
The King personally conveyed his diagnosis to both sons, and Prince William is said to Have maintained frequent communication with his father.
The Duke of Sussex, now residing in the United States, is talking with his father and making arrangements to visit the United Kingdom.
The Palace has yet to indicate the King's resumption of public responsibilities.
The feasibility of the planned official travels to Canada, Australia, New Zealand, and Samoa later this year remains to be determined.
The King's cancer diagnosis comes after undergoing treatment at a private London hospital over a week ago for a "benign" prostate problem.
On Monday, the Palace said that a distinct matter of worry was seen and ultimately identified as a kind of cancer during the therapy.
The Palace said that the King decided to disclose his cancer treatment, citing his previous involvement with cancer-related causes during his tenure as the Prince of Wales.
The Royal Society of Medicine expressed gratitude to the King for emphasizing the indiscriminate nature of cancer and encouraged anyone eligible for cancer screenings to schedule an appointment.
Simon Lewis, Queen Elizabeth II's former press secretary from 1997 to 1999, commended the King for his transparency, noting that the response would have been a brief and curt remark two decades earlier.
During an interview with Radio 4's Today program, he acknowledged that the cancer diagnosis would need significant mental and emotional effort to come to terms with. However, he expressed confidence that, based on information he received from those close to him, the individual in question would be eager to continue doing his official constitutional responsibilities privately.
50% of individuals in the UK experience the development of cancer at some point in their lives.
According to the NHS website, there are over 200 different varieties of cancer, with the most prevalent ones in the UK being breast, lung, prostate, and bowel cancer.
The incidence of several kinds of cancer rises with advancing age. According to UK statistics, the annual average shows that over one-third (36%) of newly diagnosed cancer cases occur in those aged 75 and above.
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