City of Greater Bendigo councillor Elise Chapman tweeted the image to a Bendigo woman on Sunday, writing "Oh we could have this here too? Would you like your fanny sliced off?".

The tweet was a photograph of five girls, who appear to be aged no older than two, crying as they lie on the floor with blood seeping from their wounds.

Fairfax Media has decided not to publish the image.

The woman had first tweeted Cr Chapman, writing "I hope the mosque  gets built soon, it's great to see someone who cares about all Bendigo residents and their religions".

Cr Chapman has been an outspoken critic of the mosque, and described herself as "not a fan of Islam".

"I wouldn't want to live near a mosque. Would you?" she said after council approved the mosque last year. She said at the time that under Islam, any non-believers were not worthy and should be killed.

"Every day in the media there are cases of people being raped by Muslims ... and there is no doubt a mosque would see more Muslims move to Bendigo," she said. "Islam is not a race though and I am not racist."

She later backed her comments, saying: "The people of Bendigo have every right to object to the application for a mosque without being labelled a racist or bigot."

Cr Chapman was one of only two councillors to vote against the proposal to build a mosque in Bendigo East. The developers received a planning permit in June 2014.

A group of residents are challenging the decision to grant a permit on planning and social grounds in the Victorian Civil and Administrative Tribunal.

They have also raised concerns about the impact of "Sharia Law" on their community.

The VCAT hearing continued this week, with a decision not expected for months. Cr Chapman describes herself as "proudly Team Australia" on Twitter, and writes that the views she shares are hers, and not those of the council.

She has not signed the council code of conduct, saying she does not agree with its contents.

The code states that councillors will treat all people with courtesy and respect, including "treating members of the community with dignity and ensuring that neither offence nor embarrassment are caused".

Councils must implement a code of conduct under the Local Government Act, which contains general guidelines for behaviour but makes no mention of social media.

It is believed councillors are bound by the code of conduct regardless of whether or not they have signed it.

Councillors who have their conduct questioned may have to face a Municipal Association of Victoria councillor conduct panel.

But Cr Chapman said that because she had sent the image from a personal Twitter account, and they were her own views, she did not consider it relevant that she was a councillor.

Council had not told her whether an official complaint had been made.

She repeatedly referred to an ABC article published in 2010 that was posted to her on Twitter after she had tweeted the photo. The article stated that 600 to 700 women had reported to the Royal Melbourne hospital with some form of genital mutilation in a single year.

"I don't support many things Islam does and inequality and female genital mutilation are high on that list," she said.

"We have more than 600 women presenting to one hospital with female genital mutilation each year and not one person is getting arrested for it.

"If I came at you on the street with a pair of scissors and cut your genitals, I'd get arrested for it."

Cr Chapman said that many Muslims did not assimilate into society, and that the Koran supported dangerous ideas, but she was only opposed to building a mosque on planning grounds.

"I understand that not every Muslim is a radical or a terrorist, there are some moderate Muslims. I don't know if you've read the Koran, I have and I don't agree with it."

"What is in there is very dangerous, very dangerous indeed."

City of Greater Bendigo Mayor Peter Cox said he immediately contacted Cr Chapman to express his concern about the tweet on Wednesday afternoon and had arranged to meet with her.

"Councillor Chapman's personal views certainly do not reflect that of the City of Greater Bendigo Council," he said.

"I'm disappointed that Councillor Chapman would post something of this graphic nature… I've initiated a process so we can discuss the issue.

"While councillors are individuals and are entitled to their own opinion, when it reflects on the GBCC it concerns me."

The woman who tweeted Cr Chapman on Sunday did not wish to be identified. She said she had simply wanted to show support for the mosque.

"I did not put in a complaint, although everyone was pushing for it and I was beginning to consider it," she said.

"The whole thing just really upset me though.

"I felt almost threatened, the way she spoke, the photos she shared, all from showing my own, personal support for Bendigo's mosque."

The Islamic Council of Victoria have been contacted for comment.

Cr Chapman's Twitter account was suspended about 6pm. A Twitter spokesman had earlier said he could not comment on specific cases but encouraged the reporting of offensive material.

A petition calling for the removal of City of Greater Bendigo councillor Elise Chapman from council is circulating online.