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They have already separated their working lives, with the Sussexes leaving the Royal Foundation they once shared with the Cambridges, after the Duke and Duchess of Sussex moved to a new home in Windsor from Kensington Palace.
Asked about a "rift" in the ITV documentary, and "how much of that is true", the Duke of Sussex laughed before conceding reports were not without foundation.
"Part of this role and part of this job, this family, being under the pressure that it's under, inevitably stuff happens," he said.
"But look: we're brothers, we'll always be brothers.
"We're certainly on different paths at the moment but I'll always be there for him and as I know he'll always be there for me.
"We don't see each other as much as we used to because we're so busy, but I love him dearly. "The majority of this stuff [in the press] is created out of nothing, but as brothers, you know, you have good days, you have bad days."
The Duke of Cambridge has never commented publicly on reports that the brothers are not as close as they once were.
Palace sources have previously stressed that the separation of their charity was down to their diverging working lives and future roles, with the Cambridges - as future king and queen - subject to more constraints than the Sussexes in choosing their own paths.
The Duke, who first spoke about his own mental health issues in Bryony Gordon's Telegraph podcast in 2017, also disclosed he has suffered setbacks in dealing with the pressures of living in the spotlight.
Asked how he was coping now, he said: "It's management. Its constant management as you know.
"I thought I was out of the woods and then suddenly it all came back, I suddenly realised no, this is something that I have to manage.
"Look, part of this job and part of any job, like everybody, means putting on a brave face and turning a cheek to a lot of this stuff.
"But for me and for my wife, of course there's a lot of stuff that hurts. Especially when the majority of it is untrue.
"But what we need to do is focus on being real and being the people we are, and standing up for what we believe in.
"I will not be bullied into playing a game that killed my mum."
In a clip of the show broadcast in a trailer last week, the Duke refers to the legacy of his mother's death as a "wound that festers", causing him to suffer flashbacks each time he sees a camera.
"My mum clearly taught me a certain set of values of which I will always try and uphold despite the role and the job that sometimes that entails," he said.
"I think I will always protect my family, and now I have a family to protect.
"Everything that she went through and what happened to her is incredibly raw every single day. That's not me being paranoid, that's just me not wanting a repeat of the past.
"And if anybody else knew what I knew - be it a father, be it a husband - you'd probably be doing exactly what I'm doing as well."
Asked whether his approach, and that of the Duchess, to their recent tour of southern Africa represented a "new way of doing things" in the Royal Family, he said: "I don't think there's a new way or an old way.
"We're trying to do what feels natural to us and just be authentic."
Harry and Meghan: A Journey Through Africa will air on Monday 28 Oct, 7pm, TVNZ 1.