Ryan Houghton, who stood for the party in Aberdeen North at last month's General Election, was axed as a candidate after old messages were discovered on an internet forum.
He suggested fellow users on a martial arts forum have a debate on how the holocaust had been "exaggerated by the victors".
At the time Mr Houghton refuted any suggestion he held antisemitic, racist or homophobic views, but did not deny making the comments and claimed his remarks were taken out of context.
However, the Scottish Council of Jewish Communities said the comments were "unacceptable and rooted in antisemitism".
The Tories withdrew support for Mr Houhgton in the run up to the December 12 election and axed him as a councillor.
But he remains Aberdeen City Council's business manager and vice-convener of the staff governance committee, on a £30,000 salary, an extra £13,000 on top of the basic councillor's salary.
An attempt to oust him from the job was defeated when councillors on the Tory and Aberdeen Labour administration voted it down.
At the time, the Tory group leader and co-leader of the council, Douglas Lumsden said Houghton was "innocent until proven guilty".
Writing on the forum in 2013 under the username 'Razgriz', Houghton said there is "no credible evidence to suggest the Holocaust did not happen" but that "I do find some of the events fabricated, and exegarated [sic] in some cases".
He added: "As history is written by the victors there is always going to be a bit of re-writing."
Mr Lumsden added: "I think it would be wrong for us to remove someone from their role when these are just accusations at present and they're being investigated by the party.
"The Conservative party takes things very seriously and there is a full investigation taking place."
Mr Lumsden said the Tories "look at these matters very seriously and we will look to what the outcome of the investigation is".
An SNP source told The National: "Ryan Houghton should have been suspended from the Tory council group the moment he admitted making these bigoted remarks.
"If Jackson Carlaw or Michelle Ballantyne want to be seen as anything like credible candidates for Tory leader then it's time they faced up to this issue and explained what overdue action they will take to remove Ryan Houghton from the Tory group on Aberdeen City Council for good."
Mr Houghton and the Scottish Conservative & Unionist Party have been approached for comment.
Aberdeen City Council declined to comment.