Anti-abortion campaigners say they have been ordered by the Electoral Commission of South Australia (ECSA) to stop letterboxing flyers and driving a mobile billboard around Adelaide.

Key points: Anti-abortion campaigners say they have been told to stop circulating flyers ahead of by-elections on Saturday

Anti-abortion campaigners say they have been told to stop circulating flyers ahead of by-elections on Saturday They are concerned about legislation introduced to parliament by the Greens

They are concerned about legislation introduced to parliament by the Greens Both the Greens and the anti-abortion campaigners say they have received threats over their abortion stances

The ECSA's decision comes ahead of Saturday's by-election in Cheltenham and Enfield.

It follows legislation being introduced to Parliament late last year to remove abortion from the state's crimes act.

South Australian Greens MP Tammy Franks told the ABC that she had lodged a complaint over the campaign, which compared her party's position on abortion to its stance on live export.

"...Ms Franks leads the charge, with her Abortion Reform Bill, that dehumanises and ends the lives of unborn babies — of any age, by methods far more 'cruel' and 'inhumane' than the Live Export Industry uses," the anonymous flyer reads.

The flyers also contain a photo of Ms Franks with a sign behind her with the word "killers".

"Mark Parnell and myself have taken this up because we have a by-election at the moment in Cheltenham and Enfield and under state electoral laws, we have some rules — you can't make things up, and you can't put things out that are unauthorised if they are designed deliberately to impact the electoral process," Ms Franks said.

"Nobody knew who to complain to about the materials themselves and that's why they were contacting my office to let me know."

Campaign linked to church

The ABC has identified those behind the campaign are affiliated with The Congregation at Moonta, a non-denominational church in Moonta, 165 kilometres north-west of Adelaide.

The anonymous flyer shows a premature baby. ( Supplied )

Adelaide resident Trevor Grace told the ABC he was driving the mobile billboard around Adelaide and distributing the flyers, which had been authored by the church's minister Peter Egel.

Mr Grace has previously been involved in political campaigns in South Australia, and ran for the northern suburbs seat of Ramsay, following former premier Mike Rann's retirement in 2012.

"On the truck we just have it written on there that no human beings are disposable," Mr Grace said.

He said he received a letter on Wednesday which informed the group that the truck did not meet the requirements outlined in the state's electoral laws, because it was too big, and the flyer was missing an authorisation line with an address.

"It was never our intention to interfere with an election and we weren't really aware that a by-election as such was going on — I mean, we might have been past some of the posters, but we didn't think that this had anything really to do with the by-election," he said.

"The electoral commission believes that we should desist in what we are doing or there will be hefty fines."

He said the group would consider its options going forward, including seeking legal advice.

Death threats sent to both parties

Mr Grace said the decision to keep names and addresses off the flyer was deliberate, following previous death threats made against him, and concerns about his family's safety.

Ms Franks said since she had introduced the bill before Parliament her staff had received rape and death threats.

She said any threats would be reported to police.

"When I introduced the bill, we actually had a threat of rape made against one of my staff members, which is an extraordinary threat for someone who says they're against abortion to make," she said.

"In recent days we've also had quite violent communications."

The legislation is unlikely to be debated in Parliament this month, and will eventually be decided by conscience vote after both major parties indicated they would allow one.

The ECSA declined to comment on individual cases.