It is unclear whether Meghan Markle's father Thomas will walk her down the aisle on Saturday as planned.
Mr Markle told celebrity news website TMZ, at his home in Mexico, that he had decided not to attend his daughter's wedding to Prince Harry.
Kensington Palace issued a statement saying it was "a deeply personal moment for Ms Markle".
It follows reports in the Mail on Sunday that Ms Markle's father staged pictures for a paparazzi photographer.
The widely circulated 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 Markle, Ms Markle's half-sister from her father's first marriage, has said she hopes her father will still attend the wedding.
She 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.
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."
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.
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.
Ex-Suits actress Ms Markle's father 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.
His star daughter Ms Markle has previously described him as caring, hardworking and someone who "invested in my future so that I could grow up to have so much".
She 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."
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 had earlier revealed that Miss 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.
On Sunday, Buckingham Palace released a photo of the Queen's written consent which allows the couple to marry.