Quick with a quip, His Majesty replied: "It's all done with mirrors."
Sunak added: "Well, we're all behind you. The country's behind you."
The king then revealed just how incredible the support has been regarding his recovery.
"I've had so many wonderful messages and cards," Charles said. "It's reduced me to tears most of the time."
The public learned of the king's cancer diagnosis in early February after Buckingham Palace released a statement.
"During The King’s recent hospital procedure for benign prostate enlargement, a separate issue of concern was noted. Subsequent diagnostic tests have identified a form of cancer," read the release.
It went on to reveal that the king had commenced "regular treatments" and was advised by doctors to "postpone public-facing duties".
"The King is grateful to his medical team for their swift intervention," the statement continued. "He remains wholly positive about his treatment and looks forward to returning to full public duty as soon as possible."
His Majesty chose to share his diagnosis with the public to "prevent speculation" and increase understanding for those affected by cancer.
Meanwhile, Princess Catherine has been recovering from her own health issues, having undergone planned abdominal surgery. She was discharged from hospital at the end of January, 13 days after the operation.
“The Princess of Wales has returned home to Windsor to continue her recovery from surgery. She is making good progress," read a statement from Kensington Palace at the time.
“The Prince and Princess wish to say a huge thank you to the entire team at The London Clinic, especially the dedicated nursing staff, for the care they have provided.
“The Wales family continues to be grateful for the well wishes they have received from around the world."