It is unclear whether Meghan Markle’s father Thomas will walk her down the aisle on Saturday as planned.
Meghan with her father Thomas, who is a former television lighting director.
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.
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.
It’s part of the world which Meghan Markle is joining, it’s just a rather rude and poorly timed introduction to it all.
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.