"This is a deeply personal moment for Ms Markle in the days before her wedding", it said.
Kensington Palace has not confirmed if Mr Markle will still attend the wedding, but said Meghan and Prince Harry have called for "understanding".
TMZ also said he suffered a heart attack less than a week ago.
VideoThe Clooneys, the Beckhams, Suits co-hosts. and the family of the little girl who went viral for stealing popcorn from Harry during the Invictus Games will be in attendance for the Royal Wedding. Both were expected to meet Queen Elizabeth II and other senior royals in the days before the wedding.
It was the subject of fevered speculation among royal watchers on Monday night after Prince Harry and Meghan Markle asked for "understanding" amid claims that Thomas Markle, Meghan's father, won't be attending the royal wedding.
He spent many years supervising the lighting and camera crew for the "Married... Thomas says he doesn't even drink beer. he was buying it for the guards at the place where he lives", TMZwrote. The Associated Press has been unable to reach him for comment.
And another poll by polling firm ComRes found 58 percent of respondents thought the royal wedding and the recent birth of Prince Louis to Prince William and his wife Kate were events of which Britain could be proud, although support was more pronounced among older people.
TMZ reports that Markle Sr. felt the photographs look "stupid and hammy".
Meghan's half-sister Samantha Grant admitted to arranging the staged shots of Thomas, though she insisted on British talk show Loose Women that the move was not financially motivated.
Earlier, she tweeted to say it had been her idea for Mr Markle to pose for what she described as "positive photos" to try to combat his "bad" portrayal in the press, but said it was not done for money.