51-year-old Markle told In Touch magazine that he sent his half-sister a letter congratulating her on her engagement to Prince Harry, and further apologised for all the personal troubles he had caused her.
Mr Markle was arrested following a drunken fight with his fiancee Darlene Blount on New Year's Eve. He was also arrested for brandishing a gun at Darlene several weeks earlier during another drunken fight with Darlene.
He claims Meghan never responded to his note.
Mr Markle then reached out via his lawyer to Buckingham Palace to ask for help in dealing with the extra press intrusion in his life.
'My lawyer had a phone meeting with her lawyer, and he emailed me some of her direct words. She said, ‘That’s distant family and I don’t know those people.’ That’s pretty harsh,' he claimed.
He further told the publication, 'We were as close as we could be, as tight as we could be, that’s what we were.'
Meghan's father Thomas and her mother Doria Ragland divorced when Meghan was only six-years-old.