Thomas Markle claimed in a TV interview that his daughter has shunned him since she married Prince Harry in May.
Mr Markle, 74, was due to fly over from America to attend the ceremony at Windsor, but missed his daughter's big day because of 'medical' reasons.
It came just days after he staged paparazzi pictures of himself apparently preparing to fly over for the wedding.
As his daughter gets ready to pack her bags to travel to Sandringham, where she will join the Royal Family's traditional festive gathering, her father appeared on Good Morning Britain, for the latest of a series of interviews where he has claimed he is being 'frozen out' by the Duchess.
'I'm very disappointed by it - I'm not sure why it's happening,' he told host Piers Morgan. 'I've been trying to reach out for several weeks, every day I try to text her.'
Asked if he had a message for Harry and Meghan, Mr Markle said: 'I love you very much, you're my daughter and I would really like to hear from you.
'Whatever differences we have, we should be able to work them out.'
Speaking from San Diego, Mr Markle said the rift 'can't continue forever' and he would keep trying to connect with his daughter.
He went on: 'I don't plan to be silent for the rest of my life. I love my daughter very much and she has to know that, and I would really appreciate if she would call me, just reach out to me.
'There has to be a place for me. I'm here, she knows it. I need her to reach back to me.'
Prince Harry and his wife have become the subject of intense speculation in recent weeks.
Has the Prince fallen out with his brother, Prince William? Has his wife upset her sister-in-law, the Duchess of Cambridge?
Does one or the other mean Harry and Meghan will not be staying with William and Kate at Anmer Hall? Or will the couple be staying at Sandringham House or nearby Wood Farm because the Middleton family will be staying at Anmer, meaning house room is at a premium for the Cambridges?
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