Meghan and Harry are due to Wednesday this Saturday, May 19 at St George's Chapel in Windsor Castle.
In a statement issued on Monday it called Mr Markle's comments "a deeply personal moment for Ms Markle".
Markle has been involved in controversy since it was revealed he allegedly staged a series of photos captured by an American paparazzo. She said reporters had also harassed him at his home and that he recently suffered a heart attack. Thomas Markle would walk his daughter down the aisle and her mother would drive with her daughter to the chapel.
The news comes as reports suggest Meghan's dad is no longer attending the wedding, the third reversal in just over 24 hours on a question that has thrown the wedding plans into chaos.
Our thoughts are with Thomas and the Markle family - here's hoping for a safe, successful, and uneventful surgery tomorrow morning!
Also selected for the much-anticipated event at Windsor Castle on Saturday are the couple's goddaughters and godson, and the children of one of her best friends. In order to sate their appetites for content related to the royal family, those admirers have turned to YouTube.
But Morgan did not back down and said it was the Markle family who was disappointing Meghan.More news: Romaine lettuce outbreak has spread to 32 states
Princess Charlotte, who is three.
The former television lighting director has been recovering from a heart attack he suffered last week, which left him with a "seriously damaged" heart.
Doria Ragland is a 61-year-old yoga instructor from LA, who Meghan lived with during her childhood, following her parents' divorce.
Ragland, who has reportedly already arrived in Britain, is expected to be at her daughter's side ahead of the wedding, travelling with her by vehicle to the wedding.
The Windsors Wedding Special will air on Tuesday 15th May at 9pm on Channel 4.
Markle claimed that stress about his daughter's pending nuptials had brought on his heart attack six days ago, but that he had checked himself out of the hospital so he could attend the May 19 nuptials.
"Staging those photos, that didn't seem so very bad. And the idea of contemplating him not being there now is not something that she wants to have to do".