Buckingham Palace criticized the newspaper's decision to publish on its website the private family film, which was shot around 1933, when the future Queen was only about 6 years old and as Adolf Hitler had just risen to power in Germany.
"It is disappointing that film, shot eight decades ago and apparently from (Her Majesty's) personal family archive, has been obtained and exploited in this manner," a Buckingham Palace spokesman said.
The print version of the Sun, Britain's best-selling tabloid newspaper, published a still image taken from the footage
-- showing Elizabeth alongside her mother, her 3-year-old sister Princess Margaret and her uncle, who would later be crowned Edward VIII -- on its front page with the headline, "Their royal heilnesses."
The short black-and-white clip, filmed at the royals' Balmoral estate in Scotland, shows Edward -- whom the paper describes as "Nazi-sympathising" -- apparently encouraging his young nieces and sister-in-law to perform the salute, before himself joining them.
"While there is clearly no suggestion that the Queen or Queen Mother were ever Nazi sympathisers, Edward's links with Hitler and fascism are very well documented," the article says.
The Sun also quotes a historian, Karina Urbach of the London-based Institute of Historical Research
, as describing the footage as "an important historical document that asks serious questions of the Royal Family."
Source: Queen was entirely innocent of gesture's meaning
Edward would subsequently go on to meet with Hitler in Germany in 1937, a year after he abdicated the throne in order to marry American divorcee Wallis Simpson, leading to Elizabeth's father's ascension as King George VI.
It's not clear who was filming the 17-second segment of grainy footage posted on The Sun's website. Nor does the newspaper say who provided what it says is a copy of the original film, made several years ago.
A royal source said: "Most people will see these pictures in their proper context and time. This is a family playing and momentarily referencing a gesture many would have seen from contemporary news reels.
"No one at that time had any sense how it would evolve. To imply anything else is misleading and dishonest."
The Queen was about 6 years old at the time, the source said, and "entirely innocent of attaching any meaning to these gestures."
The Queen and her family's service to the nation during World War II and the 63 years of her reign she has spent "building relations between nations and peoples speaks for itself," the source added.
Hitler was appointed chancellor of a coalition government early in 1933, and the National Socialists had been rapidly and ruthlessly consolidating their power over the government and the population that year. However, many outside Germany hadn't yet come to see Nazism as a threat.
The Sun: Images give fascinating insight
The Sun also published a separate explanation
of why it decided to run the footage, saying the images must be seen in their historical context.
"These images have lain hidden for 82 years. We publish them today, knowing they do not reflect badly on our Queen, her late sister or mother in any way," it said.
"They do, however, provide a fascinating insight into the warped prejudices of Edward VIII and his friends in that bleak, paranoid, tumultuous decade."
Elizabeth ascended to the throne in 1952 following the death of her father.
She paid her first state visit to Germany
in June, accompanied by husband Prince Philip. The trip culminated with a visit to the site of the Bergen-Belsen concentration camp
, where Anne Frank died, and which was liberated by British troops 70 years ago.