Meghan Markle’s estranged half-sister has said she hopes their father Thomas will attend his daughter’s wedding to Prince Harry on Saturday.
Mr Markle told celebrity news site TMZ he did want to walk his daughter down the aisle, despite earlier having said he would not.
This followed reports in the Mail on Sunday that he staged photographs.
Samantha Markle told Good Morning Britain he had suffered a heart attack due to stress caused by the media.
Kensington Palace has said it is “a deeply personal moment for Ms Markle”.
On Monday it was reported that Mr Markle said he did not want to cause his daughter embarrassment by attending the wedding.
This came after reports that he had allegedly staged paparazzi photographs showing him in a series of wedding-related activities – including being measured for a wedding suit – apparently unaware he was being photographed.
However, according to TMZ, he has now said he would like to travel to the wedding if doctors allow him out of hospital.
He is quoted as saying: “I hate the idea of missing one of the greatest moments in history and walking my daughter down the aisle.”
BBC royal correspondent Nicholas Witchell says there have been attempts to reassure Mr Markle he will still be welcome at the wedding.
He says Meghan Markle, 36, is close to her father and was looking forward to having him walk her down the aisle.
He said he understood Ms Markle was distressed and concerned for the wellbeing of her father, who has been described as shy and reclusive.
Mr Markle had been due to meet Prince Harry for the first time this week, as well as the Queen and the Duke of Edinburgh, before walking his daughter down the aisle at St George’s Chapel in Windsor Castle.
Samantha, who has not spoken to her famous sibling in three years – and will not be attending the wedding – told Good Morning Britain the photographs had been done with “good intention” and not for money.
She previously admitted the pictures had been her idea, in order to portray a positive image.
She said that Mr Markle, 73, had “a moral right to set the record straight and defend himself”, as the media had “raked him over the coals” and “distorted his image”.
“I wanted to see him go (to the wedding). But clearly the priority should be whether or not it’s safe for him to do that,” she added.
By Jonny Dymond, BBC royal correspondent
People around Meghan Markle are saying she is having to contemplate her father not walking her down the aisle.
The pressure has been absolutely relentless and she and Prince Harry have been concerned for some time about Thomas Markle’s mental state.
He seems to have been rather caught out by the astonishing pressure that fell upon him. Whether by design or accident he fell into this photo agency scam.
We have another example of that unhappy flipside of royalty – which is the extraordinary pressure of the media’s attention, part of it brought on by the fact the royal family require the attention of the press to maintain their relevance.
The father of the ex-Suits actress lives in Mexico and is a former lighting director who worked on programmes including the 1980s TV show Married with Children and General Hospital, for which he and his team won two Emmy awards.
He and Ms Markle’s mother, Doria Ragland, divorced when Ms Markle was six years old.
Mr Markle, who has two children – including Samantha – from his first marriage, filed for bankruptcy two years ago.
Meghan Markle has previously said: “It’s safe to say I have always been a daddy’s girl – he taught me how to fish, to appreciate Busby Berkeley films, write thank-you notes, and spend my weekends in Little Tokyo eating chicken teriyaki with vegetable tempura.”
A Kensington Palace spokesman said Ms Markle and Prince Harry “ask again for understanding and respect to be extended to Mr Markle in this difficult situation”.
The wedding will take place on 19 May at 12:00 BST at St George’s Chapel in Windsor.
On Sunday, Buckingham Palace released a photo of the Queen’s written consent which allows the couple to marry.
With five days to go, Kensington Palace revealed that Ms Markle will spend her last night before getting married at a luxury Buckinghamshire hotel with her mother, Doria.
Prince Harry will be staying 15 miles away at the Dorchester Collection’s Coworth Park in Ascot, with his brother, the Duke of Cambridge.
Meanwhile, wedding cake baker Claire Ptak, of Violet Bakery, suggested work had begun on her royal commission.