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It comes after Prince Philip was moved to St Bartholomew's Hospital to be treated for an ongoing infection as well as a heart condition.
"What is wrong with you?," the Life Stories presenter said, addressing Harry. Referring to the US TV network, CBS, he added: "If something, God forbid, happens [to Prince Philip] they'll want to exploit it."
"I think is that it is bad timing," added co-host Susanna Reid, discussing the upcoming interview on the daytime TV show.
Before Piers chimed in: "Prince Philip suffered terrible tragedies in his life, but he never gave interviews about how bad his life was."
The former journalist also said that the couple's charity venture, Archewell, offering advice on compassion ahead of International Women's Day was also "one thing that really sticks in [his] gut".
"Rather than sending out sheets, Meghan, maybe just cancel your interview because it's obviously going to cause great distress to your mother-in-law," he said.
"It's going to be a two-hour whine-a-thon," Piers concluded.
But not everyone agreed with Piers, and viewers at home had a lot of thoughts on the outburst.
Referring to his former 'friendship' with the Duchess - and his subsequent snub from the royal wedding - one wrote: "Piers Morgan's pathological obsession with Meghan Markle is a shining example of how a giant man baby with a fragile ego reacts when he perceives that someone who is completely unobtainable has shunned him. #GMB".
"Piers Morgan is such a moron, this is exactly the kind of toxicity Harry and Meghan just wanted to escape... honestly how tf can you blame them?," said another.
Piers' fury comes not long after a first look of Prince Harry and Meghan's Oprah interview dropped.
In the 30-second clip, Meghan appears to call royal life "unsurvivable" - while Harry says he feared "history repeating itself" in an apparent nod to his late mother Diana.
The talk show host stresses that "no subject is off-limits" and asks Meghan whether she was "silent or silenced" during her time as a royal.
She also suggests that Meghan, 39, has said "some pretty shocking things".
The Duchess begins the interview alone before being joined by 36-year-old Harry, who says: "You know, for me, I'm just really relieved and happy to be sitting here talking to you with my wife by my side, because I can't begin to imagine what it must have been like for [Diana] going through this process by herself all those years ago."
He adds: "It has been unbelievably tough for the two of us but at least we had each other."
The couple stepped back from royal duties last year and relocated to LA, where they are preparing to welcome their second child after tragically suffering a miscarriage.
Last week the Queen confirmed that it will not be "possible" for Harry and Meghan to return to official duties.
She said in a statement: "The Duke and Duchess of Sussex have confirmed to Her Majesty the Queen that they will not be returning as working members of the royal family.
"Following conversations with the Duke, the Queen has written confirming that in stepping away from the work of the royal family it is not possible to continue with the responsibilities and duties that come with a life of public service.
"The honorary military appointments and royal patronages held by the Duke and Duchess will therefore be returned to Her Majesty, before being redistributed among working members of the royal family.
"While all are saddened by their decision, the Duke and Duchess remain much loved members of the family."
Oprah with Meghan And Harry: A Primetime Special airs on Sunday 7th March on CBS.
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