UPDATE 7.50PM: The Bendigo Advertiser has seen screen shots of the Twitter correspondence between the woman and Cr Chapman.
The woman tweets to Cr Chapman: "I hope the mosque gets built soon, it's great to see someone who cares about all bendigo residents and their religions."
Cr Chapman then sent the woman a number of tweets containing graphic images, including one of children with mutilated genitals.
"Oh we could have this here too?" Cr Chapman wrote. "Would you like your f**** sliced off?"
The Bendigo Advertiser believes councillors are divided on whether Cr Chapman should be referred to a Councillor Conduct Panel.
Cr Rod Fyffe said he was disappointed with the tweet but had not made up his mind about whether the matter should be referred to a panel.
“I’m really disappointed with the tweet, I think we should be bigger than that," he said.
"Everyone needs to be responsible for their own actions. It’s so disappointing that this gets picked up rather than good work.
"I can see both sides of this argument and I haven't made up my mind.
“I’m undecided on what’s the best course of action at this stage.”
UPDATE 3.30PM: BENDIGO Mayor Peter Cox says Cr Elise Chapman has "come a long way" in acknowledging her actions were "not what they should have been".
He said he didn't want Cr Chapman referred to a Councillor Conduct Panel and would prefer the controversy surrounding a tweet she sent to be resolved within a week.
"There are certain things she's done that she's got to think about," he said.
"They weren't in the best interest of the council or the Bendigo community.
"Her statement indicates that's what she's thinking about.
"I would hope that things can be rectified."
Cr Cox said he didn't allow Cr Chapman to deliver her statement of apology at Wednesday's council meeting because councillors had not determined a position regarding the tweet.
He said councillors met for half an hour before the council meeting, which was not enough time to formulate a position.
"I could have allowed her to read her apology but because we had that meeting I went along with the other councillors," he said.
"I couldn't speak on behalf of the council because simply the council didn't have a position."
He said councillors would meet tomorrow afternoon to discuss the matter.
EARLIER: COUNCILLOR Elise Chapman wanted to "sincerely apologise" at Wednesday night's council meeting but lost a motion to make a statement.
During urgent business, at the end of the meeting, Cr Chapman put forward a motion to make a statement addressing the controversial tweet she sent to a member of the public.
The motion was lost and Cr Chapman did not make the statement.
However, the Bendigo Advertiser photographed a document that appeared to be the statement Ms Chapman intended to deliver.
The text reads: “Over the past week there has much attention given to a person who had challenged my position on the proposed construction of a religious facility in Bendigo.
“The comments, which were sent to my personal Twitter account, were made in explicit terms.
"I responded in similar strong terms and forwarded an image. I acknowledge, that based on the media representation of events, many people regard my comments to have not been appropriate.
“I sincerely apologise to council and the wider community.
“Some two years ago, I approached a senior officer to discuss with him the fact that I was a regular user of social media. I asked for his advice as to how to make it clear that messages..."
The remainder of the text is on another page and the Bendigo Advertiser was unable to view its contents.
Upon being told the Bendigo Advertiser would publish the contents of the statement, Chapman said the text was copyrighted and the Bendigo Advertiser was not to publish it.
However, earlier today Cr Chapman said she was disappointed but not surprised her motion was lost.
She said her fellow councillors did not tell her why they voted against the motion.
She said she wanted to apologise for the tweet.
"I wanted to apologise to anybody that was offended and offer an explanation of the facts of how it all came about," she said.
Cr Chapman said councillors would likely meet tomorrow to discuss the matter.
During Wednesday's council meeting, Mayor Peter Cox said the matter was unresolved and councillors would meet this week to determine a course of action.
"Greater Bendigo city council has tonight decided to extend discussions with Cr Elise Chapman in response to a tweet she sent to a resident on February 22," he said.
The tweet involved a graphic image of children with mutilated genitals.