Despite serving as deputy mayor since October, and then stepping up to fill the void left in the wake of Cr Richard Ziegeler's resignation from the top job, Cr Arnott said she would not be putting her hand up for the role when councillors voted next month on who the new mayor would be for the next seven months.

Crs Arnott and Otha Akoch both said time constraints prevented them from seeking the position.

Former mayor Vicki Jellie and Cr Ben Blain said there had been no discussion among councillors about who would step up.

Cr Arnott said she was very confident they would all still work coherently as a team despite the leadership change.

Cr Jellie thanked Cr Ziegeler for his work as mayor, wished him well and said she would continue to work with him.

Cr Akoch wished Cr Ziegeler well, and said the mayor's job was not easy.

"Of course, family comes first, as well as health," he said.

Cr Akoch said he was too busy to be mayor because he had a young family and was always on the road for sporting tournaments. "It's a full-time job," he said.

Cr Blain said he fully supported Cr Ziegeler's decision to stand down as mayor. "And because of his circumstances I think it is the right move," he said.

There have been signs of tension among councillors recently with Cr Blain last month moving to correct the record of a January meeting after some items were left off, including a discussion about the performance of the mayor in relation to his role in delivering the council plan and strategic direction.

"The accuracy of the information that is passed through mayor to councillors in order to be comfortable and feel informed in their decision making was questioned," Cr Blain had said.

"It appears some relationships are being strained in council because of poor governance, it is important that the public know we are working to address these issues."

Last week, the mayor also came under fire for his use of the gavel during public question time at this month's meeting where he cut off former councillor Brian Kelson when he tried to ask what he said was a clarifying question - something Mr Kelson said he was allowed to do.

Cr Ziegeler was elected mayor in October last year after serving a year as the city's deputy mayor to Cr Jellie, who had stepped into the mayoral role as a newly-elected councillor.

At the 2020 elections, it was a clean sweep as the city elected seven first-time councillors.

In his mayoral acceptance speech, Cr Ziegeler thanked the other councillors for their vote of confidence.

"I look forward to a very collegial year, another year as good as we've had with Vicki where everybody in the room of council contributes as much as they have in the past 12 months," he said.

Cr Ziegeler described his fellow councillors as being dedicated to the community without ulterior motives, politics or self-betterment.

"You're all doing it for Warrnambool," he said. "Warrnambool is my home and I want to make it as good as it can be."

Crs Angie Paspaliaris and Max Taylor were contacted for comment.

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