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.
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.”