North Shore Mayor Andrew Williams says he will make a significant announcement on Tuesday.
A group of city councillors and board members want Mr Williams to step aside, following newspaper allegations about his behaviour after drinking at a bar, including that he urinated in public.
There was no indication in Mr Williams' brief statement issued on Monday night about the nature of the announcement.
He said earlier on Monday his critics are toxic and vindictive and the allegations are a beat-up orchestrated by the ACT Party.
Five councillors have drafted a letter asking Mr Williams to resign, saying his position is untenable.
Many councillors and community board members have echoed the call, including Councillor Anne Hartley, who says Mr Williams' behaviour is his latest act of bullying and intimidation.
Ms Hartley says the mayor has often behaved in a way that is damaging to the city's reputation.
Councillor Chris Darby told Morning Report he does not know about Mr Williams' drinking habits, "but I do sense that there are some personal issues for the mayor to deal with and a number of us have had these concerns now for some time".
Mr Darby says the council has a lot of work to do during the transition to the new Auckland super-city council and does not need to be distracted by Mr Williams' behaviour.
"I think the mayor needs to throw in the towel and ... deal with those issues and allow the city to get on and do its work."
Birkenhead-Northcote Community Board chair Jennifer Yorke says the only way the council's dignity can be returned is if Mr Williams steps down.
She says a ratepayer has complained of feeling embarrassed by the way Mr Williams is treating his role as mayor.
She says he should stand down for the good of the council.
Local Government Minister and ACT Party leader Rodney Hide says he believes the mayor should step down.
However, Councillor Jan O'Connor supports the mayor and says calls for his resignation are unfair and unfounded. She believes Mr Williams is being picked on because he is outspoken.
A worker at the bar where Mr Williams was drinking says the mayor did not consume an excessive amount of alcohol on Thursday. Police say they are not investigating.
Critics toxic and vindictive - mayor
On Monday morning the mayor responded to Radio New Zealand's requests for an interview with a lengthy text message, describing his critics as "toxic and vindictive".
In the message, Mr Williams says he is not engaging any further with what he calls an ACT Party-orchestrated beat up.
Mr Williams says he has bigger fish to fry in terms of leaky buildings, the super-city and leaving the North Shore in the best possible place before the amalgamation.