The social media posts have led to the Scottish Conservatives calling for Nicola Sturgeon’s party to “disassociate” themselves from the candidate due to the “completely unacceptable” posts.
Denis Dixon, who is standing for the SNP in Edinburgh’s Sighthill and Gorgie ward, has been a serving councillor in the Capital since being elected in 2012.
The tweet, from November 20, 2018, is a reply to the then SNP MEP, Alyn Smith, who had retweeted a photo of senior Conservative Brexiteers including the former Brexit Secretary David Davis and the now-Brexit opportunities minister, Jacob Rees-Mogg.
Mr Dixon’s response said: “The Nazi movement started with 12 men in a Munich beer cellar”, followed by two emojis.
He deleted the tweet after The Scotsman brought them to the attention of the SNP on Wednesday.
Critics labelled the tweets “completely unacceptable”, with Scottish Conservative MSP, Sue Webber stating Mr Dixon had ‘made light’ of the “atrocities” committed by the Nazi regime.
Ms Webber, who served on Edinburgh council with Mr Dixon while a councillor, said: “These comments are completely unacceptable. It is shocking that any elected representative would try and make light of the horrendous atrocities the Nazis committed.
“Clearly the SNP have serious questions to answer given this individual is seeking re-election. They must disassociate themselves from a candidate who thought it was appropriate to make this hugely insulting comparison.
“Voters in his ward will be appalled at this post and will question why he has been allowed on the ballot paper again.”
The calls come after another SNP candidate was forced to apologise after admitting she did not read a personal account of racism in Scotland.
Diane Tortolano, who is standing for election in the Bannockburn ward in Stirling, dismissed the account as “a load of shit” before apologising for the “stupid comment”.
In a statement, she added: “I reacted to a headline without reading the story.
“I in no way dismiss the experiences that any individual has of racist behaviour in Scotland.”
The SNP has also faced criticism for standing another candidate in a Highland Council ward who quit the Liberal Democrats while being investigated for allegedly sharing material from the far-right group, Britain First, charges he denies.