It comes as the Metropolitan Police confirmed on Saturday it received a letter making a “number of claims” relating to Meghan’s father in 2019.
The force said it shared the letter with the Duke and Duchess of Sussex at the time, although it did not pass on the contents to other law enforcement agencies.
The Met said it is now reviewing its handling of the matter.
In a statement shared on Friday, Markle revealed the existence of the letter – saying it contained “disturbing allegations” about her father.
“I am deeply distressed,” Meghan wrote. “My thoughts are with any children who may have been harmed.”
She said she hoped it could be understood why she had largely cut off contact from her father and did “not allow him to have contact with our children”.
Meghan is the only daughter of Thomas Markle and her mother Doria Ragland.
Markle moved to the Philippines last year after he had a series of strokes.
He is reportedly now living in a Florida rehabilitation centre learning to walk again after having his leg amputated.
The Sun reported Meghan’s half-brother Thomas Markle Jnr claimed he found a stash of images belonging to his father at his former Philippines home.
He is said to have told police he discovered child abuse videos and pictures among the items. He is understood to have contacted the US Federal Bureau of Investigations (FBI) about it in July.
The FBI has since confirmed it is aware of the allegations.