Wagga mayor Greg Conkey narrowly avoided a motion to declare no confidence in his leadership on Monday evening by just one vote.
Cr Conkey said on Tuesday that councillors were still united "on the big picture".
Cr Paul Funnell brought the motion in response to Cr Conkey's remarks during last month's debate on rescinding a climate change emergency declaration, which he claimed sought to exclude councillors over their beliefs.
The motion was supported by Crs Yvonne Braid, Tim Koschel and Kerry Pascoe as well as Cr Funnell.
Crs Dan Hayes, Vanessa Keenan, Rod Kendall and deputy mayor Dallas Tout opposed the motion leaving Cr Conkey to make up the majority and block the no-confidence vote.
Neither the mayor nor any other opponents of the motion spoke during the debate but after the meeting Cr Conkey said the vote was "an issue of free speech".
"Ten days ago we had a strategic planning weekend and that was a very positive weekend where councillors talked about the future and planning over the next decade or more," Cr Conkey said.
"It was very respectful, everybody very considerate and it was how local government should operate.
"On the big picture stuff, I believe the council has stayed as one."
Cr Funnell appeared surprised when his motion was seconded by Cr Braid, saying he had "got further than I expected".
In arguing for the motion, Cr Funnell referenced Cr Conkey's comment "We can't solve all problems in our community, but we can and must plan to build a sustainable, resilient community and if you don't believe that's our obligation as councillors, I don't believe you should be in this chamber" that he made at the July 8 council meeting.
"The role of the chair person in any board or meeting structure is to neutrally guide the functions of that meeting," Cr Funnell said on Monday evening.
"The chair must at all times remain neutral and impartial in their deliberations whilst overseeing the debate.
"This does not mean they are not entitled to a personal opinion, but they must not use their position to espouse misleading, inflammatory or judgmental opinions on members of an elected body or for that matter, members of the general public."
Cr Tim Koschel said he was supporting the motion and that his main concern was maintaining unity within the council and confidence from the general public.
"This isn't a motion about climate change; it's not whether your supported or did not support change," he said.
"Everyone has their own opinions and ideas and I respect everyone's own opinions.
"Our mayor is entitled to his own opinion and he had a very strong opinion on this motion."
Cr Koschel said Cr Conkey's remarks about who should or should not be in the chamber were not "spur of the moment" but "read from a prepared statement".
"The mayor doesn't believe I belong in the chamber, along with five other councillors who voted against this motion; that's a majority of councillors who the mayor believes in his own words shouldn't be in this chamber," he said.
Cr Koschel said he "personally took offence to the comment".
"Since that meeting I have not received an email or phone call apologising for this comment," Cr Koschel said.
"Whether or not this motion passes today isn't our biggest concern.
"Our biggest concern is how we work together with a team that is divided."