In a new interview she claims the 'code of silence' since she married Prince Harry could mean Thomas Markle dies of a broken heart.
And she wants the Duchess Of Sussex to visit their father during her Stateside visit in the coming weeks.
Samantha, 53, told the UK Sunday Mirror: "I'm desperate for Meghan to meet up with Dad when she's back. If she doesn't it would be really cruel and hurtful and would break his heart.
"I speak to him every day. He's very sensitive and I see his health suffering as a result of this. I hope they can meet in a quiet place, spend some quality time together and gain closure on what's been an incredibly sad time for him.
"If they don't I'm worried he'll die of sadness. I just want her to get in touch before it's too late. Life's short – neither of them deserves to be left with the consequences."
Ex-Hollywood lighting director Thomas, 74, who suffered his first heart attack six years ago, is still recovering from the emergency heart surgery that left him unfit to travel to her wedding to Prince Harry at Windsor Castle back in May.
Samantha says her half-sister has not spoken to Thomas Markle since he publicly talked about her and Prince Harry in a British TV interview.
He apologized over the phone for being snapped in staged paparazzi photos just before Megan's wedding to Prince Harry.
And she says Meghan has also cut ties with herself and all of her other relatives on the Markle side, including half-brother Thomas Jr, 51.
She added: "Meghan needs to remember her roots – even though she's a Windsor now, she is and always will be a Markle too.
"She is Meghan Markle Windsor. Dad's done everything for Meg. He was the best dad in the world and without him she would never have achieved what she has.
"He brought her up, nurtured her, built up her character – and paid $250,000 for her education at a top private school.
"He's a dignified family man, and an incredible father. He deserves respect, not to be ignored. You don't just throw a family away like a pair of shoes."
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