Alderman Graham emailed the comments to all North Down Councillors and the County Down Spectator newspaper.
Cllr Andrew Muir said: “I am shocked to have received an email in response to this issue from Alderman Graham referring to ‘the political correct Gestapo’. To make such a reference to the Gestapo is profoundly offensive when thousands of gay men, along with millions of Jews and others were killed by the Nazis during the Second World War.
“It is vital that elected representatives use respectful language at all times. It is quite clear that Alderman Graham’s comments fall far short of what we should expect from an elected representative
“I sincerely hope that Alan will reflect upon his statement, recognise the hurt caused, apologise and withdraw his comments without any delay.
“Intolerant and irresponsible comments such as those circulated by Alderman Graham must be condemned outright. Without such condemnation, homophobia remains an acceptable prejudice which, as the evidence proves, some feel can be circulated and communicated to me in a grossly offensive manner without hindrance nor challenge.”