The Queen Mother repeats the salute, joined by Edward, and Margaret raises her left hand before the two children continue dancing and playing on the grass.
A Palace 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 is around six years of age at the time and entirely innocent of attaching any meaning to these gestures.
"The Queen and her family's service and dedication to the welfare of this nation during the war, and the 63 years The Queen has spent building relations between nations and peoples speaks for itself."
Edward, who later became King Edward VIII and abdicated to marry the American socialite Wallis Simpson, faced numerous accusations of being a Nazi sympathiser.
The couple were photographed meeting Hitler in Munich in October 1937, less than two years before the Second World War broke out.
Buckingham Palace has defended footage from 1933 that shows a young Queen performing a Nazi salute with her family at Balmoral.
The footage is thought to have been shot in 1933 or 1934, when Hitler was rising to prominence as Fuhrer in Germany.
The Sun defended publishing the footage, saying it was of great public importance and historical significance because of the involvement of the Edward.
In an editorial column the newspaper said: "Here he is, in our pictures, apparently teaching his royal nieces the same Nazi greeting he would give Hitler personally at his mountain retreat four years later."
It defended the Queen Mother and the Queen, highlighting their own patriotism and courage during the Second World War, adding: "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.
"They do, however, provide a fascinating insight in the warped prejudices of Edward VIII and his friends in that bleak, paranoid, tumultuous decade."
Military historian James Holland defended the Queen's Nazi salute as the royals playing around.
He told The Sun: "They are all having a laugh, there are lots of smiles, so it's all a big joke. I don't think there was a child in Britain in the 1930s or 40s who has not performed a mock Nazi salute as a bit of a lark."
- Independent
