The 57-year-old actor spoke in the wake of the fall out from a United States magazine interview, in which Meghan's closest friends revealed she had written to her now-estranged father Thomas Markle in August, begging him to stop talking to the media.
The Hollywood star, who with his wife Amal, a human rights lawyer, attended Harry and Meghan's wedding in May a year ago, said that history was repeating itself in the case of Meghan and Diana. "Please allow us to live our lives in peace", before adding: "Please stop lying, please stop creating so much pain, please stop exploiting my relationship with my husband".
"Oh yes, I'll be the godfather of the royals apparently", he said before laughing and confirming, "No!"
She donned a stunning a cream outfit and showed off her growing baby bump at a posh gala do at the Natural History Museum.
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And referring to Thomas Markle's decision to offer parts of a letter written to him by Meghan to a newspaper, George Clooney added "you're taking a letter from a daughter to a father and broadcasting it everywhere".
Clooney's remarks came on the same day sources close to the former "Suits" star told Vanity Fair she is "at her wit's end" over her father's decision to speak with the media despite her pleading him to stop.
"Take a look at any website, and you'll see extraordinarily abusive comments aimed not only at people in the public eye but also other internet users". "It's wrong to put anyone under this level of emotional trauma, let alone when they're pregnant", one of the friends said.
She goes on to complain that Mr Markle has made no attempt to contact her - and chastises him for falsely telling journalists he is the one who has been shunned - a criticism her father refutes.