Markle told ITV’s Good Morning Britain (GMB) that he was “hopeful something will be resolved,” adding “this can’t continue forever.
“I don’t plan to be silent for the rest of my life… I would really appreciate if she just called me,” he said.
Markle revealed he had not spoken to his daughter since they fell out in the buildup to her wedding to Prince Harry last May.
The 74-year-old missed the event due to heart surgery, amid a furore after he was found to have received payment for staged paparazzi photographs.
He ended up watching the wedding from California, with Prince Charles taking his place and walking Meghan down the aisle.
The couple are expecting their first child next year, and soon-to-be-grandfather Markle said he was “hoping that everything goes well and I get to see a little Meghan or Harry.
“There has to be a place for me, I’m her father,” he added.
Meghan, the Duchess of Sussex, has faced a barrage of negative headlines in recent weeks over her relationship with royal staff.
Her father ran to her defence, telling GMB that “she’s always been very controlling, but she’s never been rude… she’s always been polite.”