The 77-year-old also revealed that he won't try to force Meghan to allow him to meet Archie, two, and Lilibet, three months.
"What lengths would I go to to see them? I would wait patiently until they [Meghan and Harry] were ready to bring them to me," he said.
"As long as my daughter has the attitude that she doesn't want me to see them, that's the way it's going to be. I certainly won't do anything silly."
However, he went on to claim the children are being "deprived" of meeting him and seeing their other grandparents.
Thomas noted that grandparents in the US can sue for the right to see their grandchildren and said several lawyers had approached help him to do just that for free.
But the 77-year-old said he rejected the offers, adding: "To me that is like turning this into some kind of game and using them as pawns.
"They should not be used, they are just kids, babies. I will wait."
Thomas also claimed that he tried to reach out to his ex-wife and Meghan's mother, Doria Ragland, to reconnect with his daughter and her children.
His attempts were unsuccessful and he went on to call Meghan "very controlling", a comment that is unlikely to help his bid to meet Archie and Lilibet.
He gave the interview from his home, with two photos of Meghan visible on the mantlepiece behind him.
One showed the royal as a young girl, the other was a snap of Meghan with her father before she married Harry.
Meghan has not publicly acknowledged her father since 2018, shortly after her royal wedding to Prince Harry.
Their final fallout was caused by a letter Meghan sent to him begging him to stop speaking about her in the press, which Thomas went on to share with several media outlets.
A legal battle followed and Meghan, who currently resides in the US with Harry and their children, hasn't spoken to her father in more than two years.
She hasn't publicly addressed his repeated pleas to meet Archie and Lilibet.
This story originally appeared on our sister site, Now To Love.