Speaking to Good Morning Britain, the 77-year-old said lawyers had advised him he could take the couple to court to force them to give him access to Archie, two, and four-month-old Lilibet.
But he said he did not want to make the children “pawns in a game”.
Asked if he is worried about never being able to meet them, Mr Markle said: “I’m very concerned about that, I’d really love to see my grandchildren.
“People have suggested in California that I sue to see my kids and I think if I did that I’d be a hypocrite.
“I’d be doing the same thing as Meghan and Harry are doing.
“I don’t want to include my grandchildren in this kind of situation. I want to see my grandchildren with friendly parents and friendship all around.”
He added: “I’ve been told by several lawyers that grandparents have sued to see their grandchildren and won in California but I’m not going to do that.
“I don’t want to involve my grandchildren as pawns in a game, they’re not part of the game.” Mr Markle, who has not seen his daughter for more than six years, was speaking from his home in Rosarito, Mexico, 240 miles from the couple’s £1 million mansion in Montecito, north of Los Angeles.
He told the show he last tried to contact Meghan around a month ago but said he did not attempt to visit the couple’s California home for fear of being branded a “stalker”.
He said: “My message for the kids is that they have two loving families…
“It’s important for them to know that they have two families and eventually they’re going to grow up and they’re going to want to know more about them. So we’ll see what happens.”
He said Meghan’s refusal to communicate with him was “childish and silly” and vowed to continue giving TV interviews about her “until she does speak to me”.
He said: “It’s time to talk with each other, we’re family. The kids are going to grow up without knowing they have two families.
“This is more than just me and my daughter now. This is me, my daughter, her husband and two babies. So it’s time to do something. To talk.”
