The 74-year-old appeared on ITV's Good Morning Britain on Monday, where he said he hopes to make amends with his 37-year-old daughter within the next few weeks.
Thomas -- who hasn't spoken to Meghan since the eve of her wedding in May -- claims he's been texting her "every day" since and has also sent letters to Kensington Palace with no response.
"[Meghan] has always been a very controlling person and that is part of her nature, but she has never been rude," he says. "She has always been in charge."
"I've been ghosted," he adds. "I'm not sure why it's happening. I love my daughter very much. I wish she would reach out, send me a text, anything. There has to be a place for me. I'm her father."
At one point during the interview, Thomas also looked directly into the camera to deliver a message to the Duchess of Sussex, who is currently expecting her first child with Prince Harry.
"I love you very much. I would like to hear from you. Whatever difficulties we've had I hope we can work through them. We're family," he exclaims, saying he would "be grateful" for anything Queen Elizabeth II could do to help them reconcile. "I would think she would want to resolve any family problems. All families, royal or not, need to be together, especially in the holidays."
"I don't plan to be silent for the rest of my life," he continues. "I love my daughter very much and she has to know that, and I would really appreciate if she would call me, just reach out to me. There has to be a place for me. I'm here, she knows it ... I need her to reach back to me."
The interview comes just a few days after Kensington Palace released the photo for Meghan and Harry's first holiday card as husband and wife, which features a never-before-seen pic of the two watching fireworks go off at their wedding reception.
After its reveal, Meghan's outspoken half-sister, Samantha Markle, took to Twitter to share her thoughts on the card.
"Interesting that the Duke and Duchess of Sussex have their backs turned. Is this towards the world or just the Ragland and Markle family?" she wrote. "It's a bit sad. Face the Christmas spirit."
"It's incredibly rude to turn your back in a Christmas photo that is meant to share warmth and good wishes with the world. Those that criticize me for pointing out the truth, need to get that brown stuff off their noses. I hear the world's smallest violin playing," she continued in a series of tweets. "Turn your backs to people on a Christmas card is rude. If you want to be private you don't do it on a Christmas card [that] the world sees. That's like saying Merry Christmas look at my butt."
Hear more on how the royals are dealing with Meghan's estranged family members in the video below.