Watch: Thomas Markle 'pleased' by Meghan's baby news
Thomas Markle has sent the "best of luck" to his daughter and son-in-law as they welcome their second child Lilibet Diana.
Markle Snr and Meghan Markle have been estranged for some time, and were recently on opposing sides of a court battle over the publication of a note she wrote to him in the months after her wedding to Prince Harry.
But he told The Sun online: "I'm very pleased that my daughter and my new granddaughter had a successful delivery.
"I wish them all my love and the best of luck."
Markle Snr was meant to walk his daughter down the aisle when she married Harry in May 2018, but pulled out of the ceremony because he was unwell, after having heart surgery.
He was also found to have faked paparazzi photographs in his town in Mexico to make it look as though he was doing research about the UK ahead of his trip there.
In the months after the wedding, Meghan wrote a letter to him that addressed the estrangement between them. When its existence was referenced in an interview with People magazine, Markle Snr spoke to the Mail On Sunday about what his daughter had written to him.
She successfully took the publisher of the Mail On Sunday and the MailOnline, Associated Newspapers Ltd (ANL), to court over the decision to print the letter, with a judge agreeing that it had invaded her privacy and breached her copyright.
ANL is appealing the ruling.
Markle Snr said while the case was ongoing that he would be willing to give evidence against his daughter, though he has also appealed for reconciliation with her.
He has not yet met Archie, his grandson, and royal expert Robert Jobson suggested it could be some time before he meets Lilibet – noting Prince Charles will have to wait some time too.
Jobson told the MailOnline: "As it stands it seems unlikely that either grandfather will meet their new granddaughter for some time.
"Thomas is not the only one facing problems with Harry and Meghan."
After Harry and Meghan's interview with Oprah Winfrey, which was aired in March, Markle Snr called his son-in-law "snotty" and said Meghan had let him down.
Meghan had told Winfrey she felt betrayed by her father, to which he responded: "This is the first time I have heard her speak in four years. The last time we spoke, we texted, I was laying in a hospital bed after having a heart attack.
"I had to tell them I couldn't come to the wedding.
"At that point, they pretty much said goodbye, actually it wasn't quite goodbye – Harry had said to me 'if you had listened to me, this wouldn't have happened to you'."
He added: "I felt that was kind of snotty. That's the last conversation we had."
He denied that she had lost him, saying he would always be there for her, and added: "I feel she let me down."
Royal experts have suggested the choice of Lilibet as a name for baby number two represents an olive branch between the Duke and Duchess of Sussex and the Royal Family.
Relationships have been tense between the California-based couple and the rest of the royals since their step back from their duties, and strained further by the decision to open up about their experiences inside the firm, with accusations about racism and a lack of support for Meghan's poor mental health.
Daily Telegraph royal editor Camilla Tominey told ITV's This Morning: "Diana I don't think took anyone by surprise. It was a given they would give Diana as a name.
"Equally the nod to the Queen might be an olive branch.
"Maybe that is an attempt to make sure there are ties that bind across the Atlantic divide."
Former palace press secretary Dickie Arbiter wrote for The Mirror: "I’m surprised by Harry and Meghan’s choice of names for their daughter. It’s not unusual for families to name babies after a parent or grandparent.
"But given everything that’s gone on over the past few months, such as the interview with Oprah in March and Harry’s appearance on a mental health programme for Apple TV, I’m taken aback."
He added: "I wonder if taking the Queen’s nickname for his baby is an olive branch? Only Harry can answer that."
Harry is next due to be in the UK on 1 July when he will reunite with his brother Prince William to unveil a statue to their mother Diana, who they have both named their daughters after.
Watch: Harry and Meghan announce birth of daughter Lilibet Diana