It is unclear whether Meghan Markle's father Thomas will walk her down the aisle on Saturday, after he told celebrity news website TMZ that he would not attend his daughter's wedding to Prince Harry.
Ms Markle's half-sister, Samantha, has since said she hopes her father will attend if he is well enough.
Kensington Palace said it was "a deeply personal moment for Ms Markle".
It follows reports in the Mail on Sunday that Mr Markle staged pictures.
The widely circulated paparazzi photographs showed him being measured for a wedding suit and looking at newspaper stories about his daughter.
He is reported to have said that he did not want to cause his daughter embarrassment by attending the wedding.
Samantha, Ms Markle's half-sister from her father's first marriage, told Good Morning Britain the photographs had been done with "good intention" and that Mr Markle, 73, had suffered a heart attack due to stress.
She said the media had "raked him over the coals" and "distorted his image".
"He had a moral right to set the record straight and defend himself," she added.
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The ex-Suits actress's father lives in Mexico and is a former lighting director who worked on programmes including the 80s 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."
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.
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.
BBC royal correspondent Nicholas Witchell said he understood Ms Markle, 36, was distressed and concerned for the wellbeing of her father, who has been described as a rather shy and reclusive figure.
"I understand it is still very much Meghan Markle's wish that her father should be there on Saturday to support her," he added.
A Kensington Palace spokesman said: "This is a deeply personal moment for Ms Markle in the days before her wedding.
"She and Prince Harry ask again for understanding and respect to be extended to Mr Markle in this difficult situation."
The controversy surrounds pictures of Mr Markle, which were published earlier this month in a number of newspapers showing him in a series of wedding-related activities - apparently unaware he was being photographed.
Samantha Markle said it was not done for money, and tweeted: "The media was unfairly making him look bad so I suggested he do positive photos for his benefit and the benefit of the royal family."
Paparazzi photographer George Bamby said setting up photographs was "easy", telling the BBC's Today programme the only reason people do it is for money.
The wedding will take place on 19 May at 12:00 BST at St George's Chapel in Windsor.
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.
On Sunday, Buckingham Palace released a photo of the Queen's written consent which allows the couple to marry.