The King is “frustrated” about the speed of his cancer recovery and is “pushing” staff and doctors to be able to return to duties, according to his nephew, Peter Phillips.
However, Mr Phillips – the son of Princess Anne, the Princess Royal – says the monarch is in “good spirits” and remains “pragmatic”.
He made the comments during a trip to Australia where he took part in a rare televised interview, in which he praised his mother’s “work ethic” and described his family’s “huge affinity” with the country.
Speaking about the King’s recovery, he told Sky News Australia: “I think ultimately he’s hugely frustrated.
“He’s frustrated that he can’t get on and do everything that he wants to be able to do.
“He is very pragmatic, he understands that there’s a period of time that he really needs to focus on himself.
“But at the same time he is always pushing his staff and everybody – his doctors and nurses – to be able to say ‘actually can I do this, can I do that?’
“I think the overriding message would be that he’s obviously very keen to get back to a form of normality and is probably frustrated that recovery is taking a little longer than probably he would want it to.”
The King has been receiving treatment for an undisclosed form of cancer since early February, which was discovered after he was treated for an enlarged prostate.
In a further health concern for the Royal Family, on Friday the Princess of Wales revealed she was undergoing preventative chemotherapy for cancer.
During the interview, Mr Phillips, the son of Princess Anne and her first husband, Captain Mark Phillips, also praised his parents and said it was “pretty remarkable” that his mother was still carrying out overseas trips in her 70s.
“Both of them are incredibly hard-working and both in their 70s they’re still working a lot harder than either of them probably expected,” he said.
“So everyone has a huge amount to live up to and ultimately they all live by example.”
He added that Princess Anne “really valued” her home time to be able “to relax and just get to some form of normality”.
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Mr Phillips was on a visit to Australia to represent the International Foundation for Arts and Culture.
He said the Royal Family had a “huge affinity” with Australia, adding “all of us have friends over here”.
It comes after Buckingham Palace announced that the King had started treatment as an outpatient at the start of last month.
Buckingham Palace said the monarch had postponed all public-facing duties following his cancer diagnosis, but that he planned to continue with work on his red boxes of state papers.
Last month, during his first face-to-face audience with the prime minister since Buckingham Palace announced his diagnosis, the King told Rishi Sunak he had been “reduced to tears” by the “many wonderful messages and cards” he had received.
And on Thursday, during a visit to Belfast, the Queen said the monarch was “doing very well” during his cancer treatment.