The police force’s traffic account showed pictures of the men wearing SS uniforms standing next to a German military Kübelwagen on the M62 at the weekend.
Next to the images, was the caption: “These two likely lads trying to invade.”
The “shocking” image has since been deleted after sparking outrage on Sunday.
After deleting the tweet, the force wrote: “It has been removed and we will speak to those involved. It was unacceptable.”
Shulem Stern, a member of Jewish neighbourhood watch Shomrim whose grandmother is a holocaust survivor living in Manchester, tweeted his anger at the force before they removed the tweet.
Afterwards, he said: “The tweet was offensive and insensitive, there’s nothing funny about dressing up in Nazi uniform, and tweeting it from an official police twitter account makes this even more shocking.
“I’m thankful to Greater Manchester Police who took swift action and removed the tweet once it was brought to their attention.”
Others labelled the picture “disrespectful” to veterans and the Jewish community.
Officers said the men were returning from a Second World War re-enactment event in nearby Saddleworth.
The event, titled “Yanks are back in Saddleworth”, had strict instructions for any German re-enacters not to wear black SS uniforms with red arm bands.
But SS uniforms were permitted as long as the insignia was not on show.
A GMP spokesperson said: “A tweet was posted on a GMP local social media account on Sunday, August 7 which caused offence to a number of people.
“This post was deleted as soon as were made aware of it and we apologise for its content, as it was unacceptable.
“This matter has been referred to GMP’s Professional Standards Branch.”
A previous blunder from the force saw them offend many Muslims when a fake suicide bomber yelled “Allahu Akhbar” in a terror training exercise.
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