Meghan's half-brother, Thomas Markle Jr, alleged that he had found a stash of images belonging to her father, Thomas Markle Sr, at his former home in the Philippines, the Sun reports.
In an interview with the Daily Mail, Thomas Sr denied possessing child sex images, calling the accusations "sick lies".
Authorities in the UK had previously told the duchess that allegations made about her father in a 2018 letter sent to Scotland Yard and subsequently shared with her by police were being investigated, it is understood.
In a statement first reported by the Sun and issued to the Press Association, Meghan said: "I am deeply distressed at the news that has come to light in the last 24 hours, and my thoughts are with any children who may have been harmed.
"In 2018, a letter was sent to the Metropolitan Police and Royalty and Specialist Protection. That letter was subsequently shared with me.
"It made troubling and disturbing allegations against my father and I was given assurances that these were being investigated.
"I hope it can now be understood that, despite certain media publications' distortion over the years, any distance from my father and my choice to not allow him to have contact with our children, was for one reason: to protect them.
"I trusted that the authorities were doing the same for other families.
"Although the breadth of what has now been uncovered is more sickening than one could ever imagine, my sincerest hope is that justice will be fully served and that the priority remains the safety and protection of innocent children."
Meghan became estranged from her former TV lighting director father in the run-up to her 2018 royal wedding after he was caught staging paparazzi photographs.
Markle Sr did not attend the wedding, leaving the King to accompany Meghan down the aisle and meaning the only member of her family present was her mother Doria Ragland.
Meghan was the only child of Markle Sr's marriage to Ragland, though he has two children - Samantha Markle and Thomas Jr - from an earlier marriage.
In 2025, Markle Sr moved to the Philippines for a new life after suffering a series of strokes.
Then, in December of that year he had his leg amputated during life-saving surgery.
He is reportedly now living in a rehab centre in Florida, where he is learning to walk again.
The Metropolitan Police has been contacted for comment.
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