The 73-year-old, who missed Meghan’s wedding to Prince Harry because of heart problems, told The Sun on Sunday he’d not had contact with her for two months.
He said he feared dying soon without speaking to her again.
Mr Markle has since told The Sun he is prepared to fly to London without a royal appointment – and spoke of his concern that he is being frozen out of the family.
The retired lighting director pulled out of his daughter’s wedding for health reasons after he was exposed as having staged paparazzi photos of himself preparing for the big day.
He said: “If I chose in a month, or couple of months, to go to England, I want to see my daughter. I’m thinking about it.
“I don’t care whether she is p***** off at me or not.
“I’m not going to wave flags and make a fool of myself.
“I’d find a hotel room and try to reach them.”
Speaking from his home in Rosarito, Mexico, he added: “It’s sad that it’s got to this point.
“I’m sorry it’s come to this. Yes, some of it is my fault.
“But I’ve already made it clear that I’m paying for this for the rest of my life.”
He also said he wants to meet the Queen if comes to the UK, adding: “If she’ll meet Donald Trump, why not me?”
Mr Markle added: “I’d like to be treated by the Royal Family like Meghan’s father.
“I should be regarded with the respect of any other father of the bride.”
Mr Markle told The Sun on Sunday that he spoke to Meghan and Harry briefly after their wedding, but added that the phone number he had been calling Meghan on is “no longer picking up”.
He also said a Kensington Palace staff member had not been responding to his texts.
Mr Markle said: “It is probably the longest time I have gone without speaking to her ever.
“I just want to clear the air and tell her how proud I am of her.”
He added: “If I had one message for her it would be that I’m sorry for anything that went wrong.
“I’d like to put our differences behind us and get together.
“I miss you very much.”
Kensington Palace told Sky News it would not comment on the story.