Azimio leader Raila Odinga on Wednesday held talks over lunch with British High Commissioner to Kenya Neil Wigan.
The Azimio boss wished King Charles III a quick recovery as he embarked on cancer treatment.
Buckingham Palace announced that King Charles had been diagnosed with a form of cancer.
Raila lauded Buckingham Palace for sharing King Charles's condition with the public.
"The exposure will strengthen the work and resolve of those pursuing cancer treatment and management of cancer, in addition to normalizing leaders falling sick," Raila said.
Buckingham Palace said it is not prostate cancer but was discovered during his recent treatment for an enlarged prostate.
The type of cancer has not been revealed.
Buckingham Palace says the King "remains wholly positive about his treatment and looks forward to returning to full public duty as soon as possible".
He will postpone his public engagements and it is expected other senior royals will help to stand in for him during his treatment.
No further details were shared on the stage of cancer or a prognosis.
The King, 75, returned to London from Sandringham in Norfolk on Monday morning and the palace says he has commenced treatment as an outpatient.
Earlier, the King had a prostate procedure at a private London hospital more than a week ago.
The King had chosen to go public about his prostate treatment, to encourage more men to get prostate checks, the palace said at the time.
He was said to have been delighted to have raised awareness about the issue, with the NHS website reporting a surge in issues about prostate conditions.
President Ruto mourns Iran President Ebrahim Raisi