Mr Markle was countering media reports that he has not reached out to her after an unnamed friend of the duchess told US magazine People: “He’s never called; he’s never texted. It’s super painful.”
A deeply personal letter sent by the duchess to her father was published in the Mail on Sunday.
Mr Markle told the newspaper that contrary to claims made by Meghan’s friends to the media, the letter was not an attempt to resolve their rift.
He said: “I thought it would be an olive branch. Instead, it was a dagger to the heart.”
Kensington Palace declined to comment on the letter.
Five nameless friends of the duchess spoke to People in an effort to counter the “global bullying” directed at her.
Mr Markle, who allegedly staged paparazzi photos of himself days before his daughter was due to marry the Duke of Sussex, has previously claimed his relationship with his daughter has broken down.
He has made public appeals, including during an interview on Good Morning Britain, for his daughter to get in touch with him.
Meghan, who is currently pregnant, revealed in mid January her baby is due around the end of April or beginning of May.