The Duchess of Sussex is holding meetings with her closest confidantes to discuss how to deal with her father after he publicly begged the Queen to help heal their rift.
Thomas Markle has not spoken to Meghan since she married Prince Harry in May and blames the fallout on her.
He said: “I’m very disappointed by it. I’m not sure why it’s happening and I’m waiting, I’m reaching out.”
Pleading for the Queen to get involved, Thomas, 74, said: “I would appreciate anything she could do. I would think she would want to resolve family problems.
“All families, royal or otherwise, are the same and they should all be together – certainly around the holidays.”
Palace sources said the royal household had become “enraged and yet exhausted” with Thomas and believe he has “gone a step too far” by trying to draw the Queen into the row.
A senior palace source said: “The Queen is a dignified woman.
"Even if she disagreed with the way her grandson’s wife or indeed her staff were dealing with the matter, she would certainly not become involved on this level.”
Courtiers are also said to be “deeply concerned” about Thomas’s vow to carry on making public statements in a bid to reconnect with Meghan, 37, who is expecting her first child in the spring.
In the Good Morning Britain interview, Thomas said: “I’ve been trying to reach out to her for several weeks.
“Every day I try to text her. I just haven’t received any comment back. I just keep asking her to respond back to me. I haven’t got any response back. I’ve sent a letter as well.”
Despite giving an interview nearly two weeks ago, Thomas insisted: “I’ve been quiet for six months and no-one’s returned anything back to me. No one’s said a word to me. I’m confused by it.
“I’m hopeful that soon something will be resolved and we’ll be talking. This can’t continue forever.
“People are saying I should be quiet about this and not speak, if I don’t speak, they will speak to me.
“That hasn’t happened. 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.
"I would really appreciate if she would just call me, reach out to me somehow, send me a text, just say you’re there and you’re hearing me.”
Thomas has not spoken to Meghan since he colluded with paparazzi for money before her wedding in May
He said: “For that incident I’ve apologised 100 times for that. I don’t feel that that’s worthy of being shunned or ghosted – that’s ridiculous.”
Last week he accused the royals of uncouth behaviour.
Speaking of a letter he wrote to Meghan, he said: “I also pointed out the royals haven’t always been perfectly behaved. I wrote that I’ve never played pool naked, nor have I dressed up as a Nazi.”
The outburst was in reference to Harry being pictured nude in Vegas in 2012 and dressed as a Nazi in 2005.
There have been reports of a breakdown in relations between Meghan and the Duchess of Cambridge.
Actress Meghan was also labelled “Duchess Difficult” after it emerged she sends 5am emails to staff. Two of her staff have quit in recent weeks.
Thomas said Meghan had “always been a very controlling person”.
But he added: “Meghan’s always been a very polite girl. She’s never been rude to anyone to my knowledge. I just can’t see her being rude to anyone, it’s not her.”
Thomas wants to make contact before Meghan gives birth. He said: “There has to be a place for me. I’m her father and I will be the grandfather to the children, so all I can say is that I’m here, she knows it.
“I’m certainly hoping that everything goes well and they produce a beautiful baby and I’ll get to see a little Meghan or little Harry. That would be very nice and I look forward to that.
“I think she’ll make a great mum and maybe things will soften a little bit and we’ll connect again. I’ve reached out to her and I need her to reach back to me. I love her very much.”
Thomas, who lives in the US border town Rosarito in Mexico, said he would be spending Christmas Day “at the border giving candies and toys to a lot of children that have been neglected around this time of year.”
Royal insiders said the row was leading to unwelcome comparisons with Duchess of York Sarah Ferguson or Princess Diana’s involvement with the royals.
Sarah Ferguson was on holiday in St Tropez with her lover John Bryan in 1992 when paparazzi snapped her having her toes sucked on a sun lounger.
Her alleged infatuation with Texan playboy Steve Wyatt also caused concern behind palace walls.
Diana’s royal life was marked by rumours of affairs, eating disorders and clashes with Prince Charles over his secret relationship with Camilla.
A source said: “Even though the royal household is treating Meghan’s fallout with her father as a private matter, concern is circling that the situation is reaching a crisis point.”