The Duchess of Sussex’s father, Thomas Markle, says he texts his daughter every day but has not spoken to her since she married Prince Harry.
Speaking to ITV’s Good Morning Britain, Mr Markle said he did not understand why Meghan was “ghosting” him.
Mr Markle was invited to his daughter’s wedding in May but had to pull out because he needed heart surgery.
He said: “I love you very much, you’re my daughter and I would really like to hear from you.
“Whatever differences we have, we should be able to work them out.”
In the run-up to the wedding Mr Markle became embroiled in a controversy over reports he had staged paparazzi photos of himself in wedding-related activities, such as being measured for a new suit.
Speaking from San Diego in the US, he said: “For that incident I’ve apologised 100 times – I don’t feel that’s worthy of being shunned or ghosted, that’s ridiculous.”
Ghosting, an expression often used in dating, is when someone ends all communication with another person.
It was Mr Markle’s first television interview since the Duchess’s pregnancy was announced in October, the programme said.
“I’ve been trying to reach out for several weeks – every day I try to text her, I just haven’t received any comment back,” he said.
“I just keep asking her to respond back to me and I haven’t got any response back. I’ve sent letters as well.”
Mr Markle, who was not paid for the interview, suggested the royal couple could have been influenced by press reports about him.
“The unfortunate thing about my daughter and Harry is that they believe everything they read in the papers,” he said.
“For the first year they were telling me never believe those things but now they’re believing it and thinking I’m saying a lot of things that I’m not saying.”
The 74-year-old, who has never met his son-in-law, said he remained “hopeful” he would be able to meet his future grandchild, who is due next spring.
He added: “I think she’ll make a great mum and maybe things will soften a little bit and we’ll connect again.”
Mr Markle did say his daughter was strong-minded.
He said: “She’s always been a very controlling person and that’s part of her nature but she’s never been rude.
“The ghosting I don’t completely understand. She’s always been in charge, that’s her nature. But she’s always been polite.”
Kensington Palace declined to comment on the interview.