The retired TV lighting director, 74, gave an interview to the Mail on Sunday just days before his daughter celebrates her 37th birthday.
Meghan, Duchess of Sussex is already under pressure amid rumours her half-sister Samantha Markle is set to go into the Celebrity Big Brother house next month.
What has Thomas Markle said about Meghan in new claims?
Thomas Markle Snr claims his daughter has shut him out of her life since he staged fake paparazzi shots ahead of her royal wedding to Prince Harry, 33, in May.
He said: “I’m really hurt that she’s cut me off completely.
“I used to have a phone number and text number for her personal aides at the Palace, but after I said a few critical words about the Royal Family changing Meghan, they cut me off.”
He went on to say he would have liked to have sent his youngest child a birthday card but if he sent one to Kensington Palace it would be “one among thousands”.
What else has Thomas said about Meghan?
Thomas, who spoke from his home in Mexico, accused Meghan of having a “sense of superiority” and said he feared being deprived of a grandchild.
He said: “What’s sad is that some time in the next year Meghan and Harry will have a baby and I’ll be a grandfather, and if we’re not speaking I won’t see my grandchild.
“How tragic is that, to deprive a child of its grandfather because I said a few things critical of the Royal Family?”
Mr Markle stated he had “just about reached my limit with Meghan and the Royal Family” and said he refused to be “silent”.
He added: “I refuse to stay quiet. What riles me is Meghan’s sense of superiority. She’d be nothing without me.
“I made her the Duchess she is today. Everything that Meghan is, I made her.”
He also had sharp words for Prince Harry saying he did not care if he spoke to him again – adding Harry’s mother Princess Diana would have “loathed” how he had been treated.
Has the Royal Family responded?
A Buckingham Palace spokeswoman told Express.co.uk they would not comment on what Mr Markle had said.
But this is not the first time Mr Markle has come under fire for making comments about Meghan and the Royal Family – and his latest interview is likely to cause them embarrassment.
Earlier this month, US media claimed the Duchess had refrained from communicating with her father for fear of her words being leaked to the press.
A source told US Weekly: “Meghan is so upset over Thomas. She’s upset for a couple of reasons.
“She doesn’t even know how to communicate with her dad without knowing he won’t exploit her.
“She lives in fear that he’ll leak their communication. If he’s spoken this much already, why wouldn’t he leak their conversation?”
The former actress has previously described herself as being a “daddy’s girl”.
But speaking in the interview about how this changed, Mr Markle referred to his ex-wife Doria Ragland as being the preferred parent.
He said: “Oh, she’s a mummy’s girl now, and Doria gets a lot of the credit.”
Kensington Palace also told Express.co.uk it would not comment on Mr Markle’s remarks.