GetUp has accused the Liberal senator Eric Abetz of emailing its members with misinformation, after the senator sent out a mass email claiming the progressive activist group was endorsing a “crook and a white supremacist” in the Longman byelection.

In an email sent to many GetUp supporters on Wednesday, Abetz claimed that GetUp had endorsed the Australia First candidate, Jim Saleam, over the Liberal candidate in the byelection. Saleam founded the white nationalist group National Action in the 1980s.

The basis of the claim was an article in the Australian noting that GetUp phone volunteers’ call sheets urged voters to “put Trevor Ruthenberg and the LNP last on your voting ballot”.

Followed strictly, those instructions would result in Saleam receiving a higher vote than Ruthenberg, although GetUp did not endorse Saleam and preferences would only affect the result if the Australia First candidate survived deep into the count.

Abetz claimed the message exposed “GetUp’s truly ugly underbelly and their real reason for existence – to defeat the Coalition at any cost with any lie and and any excuse for its gross dishonesty”.

“I have demanded that GetUp explain the use of supporters money for this nefarious purpose and as a donor to GetUp I ask that you raise concerns with the organisation,” he said.

GetUp responded in an email to members that the claims were “outrageous” and based on “a misleading beat-up in the Australian”.

Regarding alleged support of Saleam, the GetUp spokesman said “nothing could be further from the truth”.

“The history and positions of that candidate, Jim Saleam, are abhorrent and in direct contradiction with the values of any decent society.

“Accordingly, he is appearing dead last on our how-to-vote guide in Longman.”

GetUp’s how-to-vote card suggests giving Ruthenberg the number seven preference, behind the Greens and Labor at spots one and two, but ahead of Pauline Hanson’s One Nation (10) and Saleam (11th and last).

GetUp’s spokesman explained that Abetz had obtained email information from a campaign about Abetz’s call for the Australian Securities and Investment Commission to investigate the group. GetUp members who took part responded with a donation to GetUp and an email to “tell Abetz that his attacks inspired you to donate”.

“Of course, whenever any one of us emails a politician, they have our email address so they can respond.”

The GetUp spokesman said that rather than “respond thoughtfully” to individual voters, Abetz appeared to have added its members “to a mass email list without your consent”.

“Still, we’re very sorry if your inbox is being invaded by Abetz in this way.”

GetUp set up a form to allow members to contact Abetz to ask to be removed, but noted that “technically he may not have to” because political parties are exempt from certain rules on privacy and spam.

Abetz told Guardian Australia that he was glad that “following pressure, GetUp has decided now to put the white supremacist last”.

He accused GetUp of a “double standard” for “directing their members to spam my inbox with tirades of abuse yet cry foul over me sending one email drawing their members’ attention to news reports”.

“Keep in mind, the email addresses were all provided to me by GetUp.”

Abetz said he would respect the wish of anyone who did not want to receive communications, adding “I expect that courtesy will be a two-way street.”

“But consistency has never been a strong suit of GetUp activists.”

One GetUp member, John May, said he “can’t really complain” because he had contacted Abetz and didn’t want to blame GetUp either.

But he said he was upset with the way Abetz had used the email, adding “I can’t help but feel that his email is counter-productive, because anyone who is a GetUp member likely wouldn’t be voting for the LNP anyway.”

Ben Packham, the author of the Australian’s report , said on Twitter it was a “legitimate story”.

Guardian Australia has contacted GetUp for comment.