The department passed on two messages to Downing Street in the weeks leading up to the event, which were then ignored, leading to the worst election campaign blunder of the last 14 years.
The claim is contained in Blue Murder, by the Daily Telegraph's political editor, Ben Riley-Smith.
The Guardian has also spoken to sources about that day's events.
According to the book, the Foreign Office provided written advice on two occasions before the event telling Downing Street that the prime minister should attend.
The first came a few weeks before the event and the second just a few days before, once it became clear that Keir Starmer would be attending, as would the Ukrainian president, Volodymyr Zelenskiy.
One source spoke of "very clear advice from the department that it would be an important event to go to and there would be significant risks should he not attend".
Having endured a difficult start to the campaign, Sunak had regained some momentum with a combative first debate performance against Starmer. But as the 80th anniversary D-day commemoration approached on 6 June, his senior team had no sense of the PR disaster about to engulf them.
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