The Duchess of Sussex's father, Thomas Markle, says his daughter cried when he told her he would not be able to attend her wedding to Prince Harry.
In an interview with ITV's Good Morning Britain, Markle discussed his relationship with Meghan and his new son-in-law.
The 73-year-old former television lighting director said he broke the news that his health would prevent him from making the journey just days before the ceremony in Windsor Castle last month.
"Meghan cried, I'm sure, and they both said 'Take care of yourself, we are really worried about you,'" he said.
"I absolutely wanted to walk my daughter down the aisle," said Markle, who watched the wedding from California, where he was recovering from heart surgery just days after allegations surfaced that he had staged photographs with the paparazzi.
"I realized it was a serious mistake," he said of the photos. "It's hard to take it back."
He said the royal couple were "very forgiving," and at that point he was still on track to go to the wedding.
"Meghan said 'everything is ready for you', Harry said 'I've got one of my military friends to take care of you'. It was all set up. It was fine."
"The truth is I couldn't get over the fact that that had happened -- that all that stuff was working on me, I had a bit of a heart condition, this pushed me a little further to the point where I had heart palpitations, I had to go and drive at two in the morning to a hospital in Rosarito [Mexico] to the hospital, and they sent me to another little hospital and then they sent me to a bigger hospital in Rosarita, the General Hospital, and I had a heart attack.
"The hospital stabilized me... but after about a day and a half in that hospital, I said I feel better and I want to go and I wanted to check out now. I want to go to the wedding. I had to have myself signed out and had to leave on my own against their wishes but I checked out and I thought I was better."
Markle said he talked to Harry and Meghan and at that point, he was still set to go to the wedding.
"I got a call from a guy ... who was assigned by Harry, I think. He said, 'we are going to take you tonight.' At that time I started getting heart palpitations and I started getting chest pains and I said I have to cancel. And that was because I didn't take care of the heart problems before, so I had another friend take me back across the border to a hospital in the States where I was told my condition was very bad and I had to operate and so I had heart surgery."
In the end, he watched his daughter's wedding hiding from the press in a small room in a bed and breakfast.
"I was very upset it wasn't me, because the whole world was watching my daughter. The unfortunate thing for me now is I'm a footnote in one of the greatest moments in history rather than the dad walking her down the aisle."
When asked about how he felt when Prince Charles, Harry's father, stepped in for him, he said: "I can't think of a better replacement than someone like Prince Charles. He looked very handsome and my daughter looked very beautiful. I was jealous ... I wish it had been me, but thank God he was there and I thank him for that."
Markle said Harry asked for his daughter's hand in marriage over the phone and that he has had several conversations with the British royal.
"Harry got on the phone with Meghan -- they called me together. Harry asked for her hand on the phone and I said, 'you're a gentleman. Promise me you'll never raise your hand against my daughter."
Of Harry, Markle said: "He's quite easy to talk to. He's a very comfortable person to talk to. I wasn't nervous. Ten thousand miles apart it's hard to be nervous."
And with regard to the huge social gap his daughter would have to straddle he said: "The royals are very complicated. It's a whole different lifestyle but I think she can always rise to that occasion. My daughter is capable of anything and she'll certainly be a compliment to the royal family.
He described Meghan "as a prize for him (Harry) as well."
He said of the fact his daughter would be the black member of the British royal family in modern history: "I think it's long overdue. I think there shouldn't be any color barriers anywhere. I think its an improvement on the royal family. It's an improvement for England."
Markle said he also discussed the US President with Harry. "I was complaining I didn't like Donald Trump. He said, 'give Donald Trump a chance'. I sort of disagreed with that."
When asked if he thought Harry was a Trump supporter, Markle replied, "I would hope not now, but at the time he might've been."
On the subject of the UK leaving the European Union, or Brexit, Markle said: "It was just a loose conversation about something we have to try. There was no real commitment for it. I think he was open to the experiment."
Markle said he still hadn't met any members of the family his daughter has married into.
"It's going to have to work out for them and me as well. I know they are very busy," he said. "I would love to meet the Queen. I have had respect for that woman since I was a child."