The 75-year-old was filmed leaving a shopping centre near his house in Rosarito, Mexico, on Monday when a reporter asked whether his daughter Meghan “has the right to use the word royal”.
He briefly hesitated before responding: “I'm very upset with Meghan and Harry right now. I don't think they have the right to use the word royal."
His comments follow news that the couple will drop their use of the “Sussex Royal” brand for their charity and commercial activities once they step down as senior members of the Royal Family on March 31.
He added: “I don't think they have a right to speak to the Queen in the way they have spoken to her, I think it's an insult to the Queen and to the British people.”
The couple, who have relocated to Canada, have abandoned plans to trademark the label, stating on their website: “It has been agreed that their non-profit organisation will not utilise the name ‘Sussex Royal’ or any other iteration of ‘Royal’”.
However, they added that they had made the decision despite there not being “any jurisdiction by The Monarchy or Cabinet Office over the use of the word ‘Royal’ overseas.”
Mr Markle continued his criticism of the duchess, saying: “My daughter dumped me one day before she got married, she has dumped my family, she has dumped Doria's family, she has dumped every family and now she is dumping the British family.”
It follows a number of TV appearances in which the 75-year-old criticised Meghan for her alleged treatment of him.
In an interview on ITV’s Good Morning Britain in January, Mr Markle called the couple's decision to stand down as senior royals and move away from the UK "embarrassing."
"They married into royalty, they knew what they were getting themselves into," he told the programme, speaking live on air for the first time since their relocation.
"I think they've hurt the Queen, they've hurt the royalty. I'm a little embarrassed for them and feeling very sorry for the Queen."
His remarks yesterday came as the duke prepares for his final round of official engagements before stepping down.
Harry was pictured arriving in Edinburgh on Tuesday evening in advance of a summit focusing on his sustainable tourism project, Travalyst.
The duke founded the Travalyst coalition along with brands including Booking.com, Skyscanner, Tripadvisor, Trip.com and Visa.
Around 100 people from the tourism and travel industries have been invited to join the working summit, which he will host.
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