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On Tuesday afternoon, Sir Tim said councillors "leapt forward in unity" at a closed meeting to launch the vote, before they stormed out.
The same time the meeting began, Local Democracy Reporting received an email from the mayor which described the council as a "regime".
The email was in response to questions raised about Sir Tim storing personal items in council-owned buildings across the city.
Sir Tim conceded that the message had been written by partner Asha Dutt, and that its contents were not well-received.
He was adamant attendees wanted him gone, but was not clear on how they had gained access to his personal email.
Cr Nobby Clark, who has had a tenuous relationship with the mayor since becoming his deputy, was present at the meeting and said Sir Tim’s version of events were incorrect.
Cr Clark said the chairs group asked the mayor to withdraw the comments made to media because it felt they were dishonest and left a staff member open to unfair criticism.
When he refused to do so, Sir Tim was told his behaviour could lead to further action.
"I personally said to him at that meeting, you cannot continue to distort the truth when it comes to this council.
"We have more important issues to resolve."
Cr Clark also warned the mayor his actions were heading him in the direction of a vote of no-confidence, he said, but any such action would have to go through the full council.
Speaking after the incident, Sir Tim responded to a question about whether he would resign over what had happened with, "Hell no", and said he wasn't going anywhere.
"Well, I’m going to take Declan [my son] to music lessons. I’ll do my best to promote the city as much as I can. These threats made against me will not put the city in a good light."
Although the media response had been written by his partner, Sir Tim said he normally formulated his own replies.
"I’m not very good with technology so I dictate to her and she sends it off.
"That irritates them [other councillors] immensely, but, well, it’s just the way I operate."
It has been a tumultuous ninth term for New Zealand’s longest-serving mayor.
In October last year, an independent review highlighted a "leadership void" with Sir Tim at the helm.
In May this year, it was revealed he had lost his driver's licence, but he never revealed why.
The following month, Sir Tim opened up about a health condition he had developed called muscle tension dysphonia that was affecting his ability to "defend" himself.