Ahead of the meeting councillor Linda Cooper said she really hoped the mayor would get how the councillors and Aucklanders were feeling about his behavior.
Councillor Mike Lee said he had been in local government for 21 years "but this is a new experience for me and I will have to take it as it comes".
"It is not in Auckland's interest that the mayor resigns but clearly the mayor has a lot of work to do to rebuild trust."
Mr Brown issued a statement this morning after he left the meeting, which continued without him.
"We had a full, frank and robust discussion and I have offered a full and unconditional apology to Councillors.
"I understand the frustration and disappointment that Councillors feel. I realise that I have a good deal of work to regain their trust and rebuild our working relationships in the interests of Auckland. This is my focus, starting today."
- Brown refuses to pay part of inquiry bill -
Meanwhile Mr Brown says he will not pay any of the $100,000-plus costs of a damning review that found he failed to declare more than $39,000 in free hotel rooms and upgrades.
Mr Brown said he supported the review by council chief executive Doug McKay and agreed to the terms of reference, which cleared him of using council resources or providing preferential treatment in connection to his affair with Bevan Chuang.
But when it came to costs arising from the rest of the inquiry that found he received nine free hotel rooms worth $6130 and 64 upgrades worth $32,888.50, Mr Brown said that was something Mr McKay had pursued.
Mr Brown said he he would pay his personal costs for legal advice from Philip Skelton, QC, but would not pay any costs of the review.
Mr McKay has estimated the cost of the EY (Ernst & Young) review at $100,000-plus. Other associated costs include legal advice to the council by Crown Solicitor Simon Moore, QC.
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Read the full report here.
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Last night, councillor Chris Fletcher said Mr Brown should have to shoulder some of the costs of the review once the bills came in.
The right-leaning Mrs Fletcher and left-leaning Mike Lee are planning a cross-party motion at Thursday's council meeting to establish a monitoring committee to oversee the mayor and his office.
Mr Brown has never apologised to the council for the two-year affair and showed little remorse on Friday when his free hotel rooms and upgrades were revealed.
Auckland interest groups have mixed views on his behaviour.
Problem Gambling Foundation chief executive Graeme Ramsey said the revelation Mr Brown took three free hotel nights and five upgrades at SkyCity hotels on top of a $15,000 donation from the casino company during the 2010 local body elections showed the company had deliberately gained his favour. "I don't think anyone can believe he can be impartial from this point onwards in any dealings with SkyCity," Mr Ramsey said.
Employers and Manufacturers Association chief executive Kim Campbell said Mr Brown was a good leader and should stay.
