Cr Dixon was sentenced in the Gore District Court last Wednesday to community detention after admitting assaulting his partner Janice Paterson and her 16-year-old daughter at their home in Mataura on May 15. The pair have since separated.
He was also ordered to pay $3895 reparation.
Cr Dixon did not speak on the matter.
Gore Mayor Tracy Hicks told Cr Dixon he did not expect him to make a decision straight away. It is unclear when Cr Dixon will announce his decision.
Mr Hicks told the meeting the council had to decide if it was "appropriate" for Cr Dixon to remain a councillor.
"I have no wish or desire or intention to allow any debate around this table about the appropriateness or otherwise of the conviction."
Mr Hicks said he had suggested to Dixon if he was in a similar situation he would resign, but Cr Dixon had indicated he was unwilling to do so.
Cr Dixon avoided the possibility of being automatically removed from the council when police amended the charges from assaulting a female, which has a maximum penalty of two years' jail, to assault, with a maximum of one year's jail.
Under the Local Government Act, an elected representative is automatically disqualified from office if convicted of an offence carrying a penalty of two years' jail or more.
"I am sure that councillors are aware that there is a threshold if a councillor is to be stood down from their position. Cr Dixon does not meet that threshold," Mr Hicks said.
In a letter to the council, Cr Dixon said since his "wrongdoing" was made known, many Mataura people had encouraged him not to resign.
"I was and am wrong and I wish there was a replay button that I can correct what happened that night. But we all know that there is no replay and we have to live with our mistakes," he said.
"I believe that my life as a councillor is not yet over ... I would like to stay on and do my best for the council."
Cr Ralph Beale said he was "appalled" by Cr Dixon's actions.
"There is a big percentage of people out there who say the Gore District Council is back to where the council was a few years ago - a bit of a shambles."
Cr Anne Gover said if she were in Cr Dixon's position she would resign and stand again in a by-election to give Mataura people the chance to support him.
Cr Graham Sharp told Cr Dixon he did not condone what he had done but knew he regretted his actions.
Only one councillor, whose name was not recorded, voted against Mr Hick's motion to ask Cr Dixon to resign.
