Meghan Markle was asked by the Queen about her opinion of Donald Trump the first time the two women met, Prince Harry has written in his memoir Spare.
The Duke of Sussex said introducing his grandmother to his now-wife Meghan was "pleasant" and the late Queen looked "pleased".
During the meeting, which took place at Royal Lodge, the Duke of York’s Berkshire home ahead of the 2016 United States presidential election, Queen Elizabeth II asked Meghan about Trump, but she quickly changed the subject.
Writing about the encounter in his book, Harry said: "It was all very pleasant. Granny even asked Meg what she thought of Donald Trump
"Meg thought politics a no-win game, so she changed the subject to Canada."
The Duke of Sussex said his grandmother "squinted" and told Meghan "I thought you were American", to which Meghan replied: "I am, but I’ve been living in Canada for seven years for work."
The book added: "Granny looked pleased. Commonwealth. Good, fine."
Harry said that after about 20 minutes, the Queen had to leave and was escorted by Prince Andrew, according to the Independent.
He told how the former Suits star did not recognise the Duke of York, who was holding the Queen's handbag when he joined them, and thought he was the monarch's assistant.
Spare, which hit the shelves on Tuesday, was boosted into the record books with 400,000 hardback, e-book and audio format copies being snapped up, its publisher said.
The book included claims that the Prince of Wales physically attacked him and teased him about his panic attacks, and that the King put his own interests above Harry's and was jealous of the Duchess of Sussex and the Princess of Wales.
In a US broadcast promoting the work, Harry branded Duchess of Cornwall the "villain" and "dangerous", accusing her of rehabilitating her image at the expense of his.
Larry Finlay, managing director of Transworld Penguin Random House, said: "We always knew this book would fly but it is exceeding even our most bullish expectations.
"As far as we know, the only books to have sold more in their first day are those starring the other Harry (Potter)."
As the duke continued a run of high-profile promotional interviews, he said he "would like nothing more" than for his children to have relationships with the Royal Family.
His remarks about his son and daughter came despite the criticism he has levelled at his brother William, father Charles, and stepmother Camilla.
In his first print interview about his autobiography, he told US magazine People that Archie, three, and 19-month-old Lili did have a connection with some of the Windsors, whom he did not name, saying this brought him "great joy".
He also described his late mother, Diana, Princess of Wales, as his "guardian angel" and said she is with him "all the time".
