SNP Women's Pledge, a group which has grown out of a petition calling for a debate around gender self identification, responded to a story in the Herald on Sunday about a signatory allegedly using derogatory language about a trans woman.
The petition currently has more than 2,700 signatures.
Marjory Smith, the party's women's officer in Nairn, reportedly referred to the trans woman as looking like serial killer Ed Kemper, and saying trans activists were "possessed by an evil, dangerous cult".
The comments were made in messages sent to Emma Roddick, an SNP candidate for the Inverness Central council ward.
In a letter from Women's Pledge, the group said Ms Smith was trying to get Ms Roddick to sign the pledge, which she refused to do.
The letter also said Ms Smith was "fearful for her personal safety" as a result of the Herald on Sunday story, and called for Ms Roddick to be sanctioned by the party.
The letter said: "We are shocked that Ms Roddick used the media to attack an ordinary party member who approached her privately with concerns that were shared by other branch members.
"Ms Smith is not a public figure, she is a volunteer who works hard for the party and who is now fearful for her personal safety as a result of this smear story.
"We believe that in approaching the media about another member's internal correspondence and revealing her own complaint to the media, Ms Roddick has breached the party's code of conduct and should be disciplined.
"We note that the Cabinet Secretary Shirley Anne Somerville has said that women who express concerns about sex self ID should not be subject to knee jerk accusations of transphobia.
"This is exactly what Emma Roddick has done in betraying Ms Smith's confidence and subjecting her to a hate campaign in the media."
In response to the Herald on Sunday story, Ms Smith said attempts to enshrine self identification in law was "totalitarian and fascist", adding: "At least theJehovah's Witnesses just go away when you won't take a leaflet".
Ms Roddick reported Ms Smith to party bosses.
She told the Herald on Sunday: "It is really worrying that this debate has been allowed to get to the point where a women's officer within the SNP feels they are able to say things like this. If we had nipped this in the bud earlier instead of hoping it would all go away, we wouldn't have got to this point."
The debate on gender self identification has raged within the SNP in recent years, with reports surfacing of a number of members who have considered leaving the party over the issue.
Signatories of the pledge assert rights they believe all women should hold, including to discuss policies without abuse, maintaining female-only spaces and refusing male access to such spaces.
An earlier version of this story incorrectly stated Emma Roddick was a councillor and that she sent the comments to the Herald on Sunday. Ms Roddick is a candidate for the Inverness Central council ward. Ms Roddick says she was approached by the Herald on Sunday who already had the remarks and contacted her to comment on them. We apologise for the error and are happy to correct it.