"And the correspondence I got back was [that I was] 'distant family and I don't know those people'.That came from Meghan," he alleged.
He also said he didn't "100 per cent" buy Meghan's claims during her interview that she had mental health problems
The scene aired after he issued an apology to Meghan for criticising her in the media, saying he'd "made some horrible mistakes" when she started dating Harry.
He said he was on Big Brother VIP so that Meghan might watch and "see the real me".
"I want everybody watching to take away this side of me, the real me. I am lovable, nice, I'll give you the shirt off my back, I'm funny," he said.
Despite previous warnings to Harry that Meghan would "ruin his life," Markle said there was no bad blood on his side.
But he claimed that the sibling relationship went south when she started dating Harry, throwing him "to the wolves" with "no experience" of dealing with the press.
"I was being backed into a corner, into a wall. I made some horrible mistakes and still regret them to this day," he said.
Markle insisted that he loves Meghan and would "do anything" to meet his nephew Archie and niece Lilibet.
"I don't need a photo-op to go see my sister, and I don't want a story behind it ... I don't want anything, I would just love to go over to their home and knock on the door, give her a big hug and kiss, and say I missed the hell out of her and apologise right to her face.
"Maybe one day that will happen. I'd do anything to see Archie and Lilibet."