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.
TMZ reports that Mr Markle suffered a heart attack a week ago, although this has not been confirmed by the family or palace.
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, Ms Markle’s half-sister from her father’s first marriage, has claimed she is to blame for the photographs.
“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.
“We had no idea he would be taken advantage of. It was not for money,” she tweeted.