A high-profile opponent of Len Brown cancelled a meeting with the mayor and said he should resign in the wake of the sex scandal.
Cameron Brewer was re-elected unopposed as the councillor for the Orakei ward and was announced as the running mate of right-wing mayoral candidate John Palino two weeks before votes were counted.
Mr Brewer has declined to comment since news of the affair broke last Tuesday, but the Herald can reveal he cancelled a meeting with the mayor last week.
He also sent texts to Phil Wilson, Mr Brown's chief of staff, and David Lewis, his communications strategist, to say the mayor should resign.
A spokesman for Mr Brown would not release any correspondence sent by councillors, but said the mayor had meetings with all but two and the "tone in general was highly supportive".
The two councillors who declined to meet Mr Brown were Mr Brewer and fellow right-wing member Dick Quax.
"Mr Brewer passed on a message earlier in the week that indicated the mayor did not have his confidence," said the spokesman.
Mr Brewer confirmed he had made his "private views" known to Mr Wilson and Mr Lewis, "both of whom I respect and know pretty well".
"However, I will continue to make no public comment on the wider issues in light of the independent review that is now under way.
"I just really want to focus on doing my bit for Orakei ratepayers, which includes promoting local projects and pushing for lower rates, debt, and council costs.
"That is where my focus has been for the past three years and that is where it remains."
Mr Quax last week said that the mayor's affair with Bevan Chuang was more than a personal situation.
"This is Len's second indiscretion. The first one was with credit card spending at Manukau City," he said.
Mr Quax could only see Mr Brown now being a lame-duck mayor for the next three years.
Meanwhile Mr Brown says the people of the city want him to "get on'' with the job in the wake of his extra-marital affair scandal.
Mr Brown told Radio Tarana this morning that Aucklanders "are of the view that we need to get on - and that's certainly my intention.
"I think Aucklanders generally like the direction in which we're going and respect the leadership I've given thus far in my role as Mayor of Auckland.
"So I think it's critical that having gone through what we went through, in terms of my private life, last week that we get on with the public life, the business of Auckland, and keep moving Auckland forward.''
He said most of the sitting councillors were supportive of him maintaining his role, saying they understand the situation because they're also in the public eye.
''[They] understand the importance of maintaining some degree of respect for people as they go through their trials and tribulations in life, no matter who they are,'' he told the Indian radio station's breakfast show.
"I think for the councillors really the message from their community is, 'get in there, get on with the job, build our communities, make them a better place, look after us and do the job that you're elected to do, stop mucking around'.''
Mr Brown admitted that the election, held on October 12, felt like it had happened "about 10 years ago now''.
He said he was committed to his key issues of improving transport in the city and developing affordable housing.
He also told the station he was "confident'' the review into his expenses and use of council resources during his affair with Bevan Chuang would show he did not abuse his position.
As the interview closed, Mr Brown was asked what message he had for the Hindu community in the city as they prepared to celebrate the Festival of Lights, or Diwali, with its focus on forgetting the past and looking to the future.
After a small laugh, Mr Brown said: "I think it's always important to learn from lessons of the past and my message is, for me personally and my family, you've got to be able to move on from your mistakes, learn from them, and try to become better men, better women and better communities.
``Hopefully I can prove that through my actions.''