Redland City councillors are disappointed by the negative attention Mayor Karen Williams has brought on the Council after she was found guilty of drink driving.
Councillors Adelia Berridge and Wendy Boglary have spoken out after the mayor's punishment was handed down in court on Monday.
They say the mayor has displayed poor leadership.
Cr Williams' driver's license was disqualified for six months. In addition, she was ordered to complete 80 hours of community service when she pled guilty to high-range drink driving after crashing her car into a tree at Cleveland in June.
No conviction was recorded and the mayor said she would return to work "later this week."
Cr Berridge has been a vocal advocate for Cr Williams' resignation and attended protests at Council and in front of the Cleveland Magistrate's Court alongside frustrated residents.
She said the mayor was being irresponsible by staying in the city's top job.
"Now, the mayor has publicly admitted her DUI, has had her day in court and a month to think about her responsibilities and expectations as a civic leader. I hope she sees the most responsible thing to do today is resign and bring the embarrassing, negative attention to an end so we can move forward," Cr Berridge said.
She said her resistance was setting a bad example for other Councillors.
"I can't reconcile how the Mayor's office organised a meeting with parents feeling the deep pain of losing a child and advocating that she would lead the charge for stronger education and laws, while shown to be very intoxicated during that meeting," she said.
"That's the definition of hypocrisy. Civic leaders set the benchmark for Councillors to follow. I can't follow that standard."
Cr Wendy Boglary has also questioned the mayor's ability to lead Redland City Council and said her leadership had been tested.
"Good leaders know when to step up. Good leaders know when to step down," Cr Boglary said.
"One of the fundamental elements of leadership is respect. Respect of those you lead and respect those with whom you interact.
"Respect is earned. It is not an automatic right regardless of the title or position or who you think you are. This is now a test of leadership."