Asked if he thought Mr Brown should resign, Mr Quax said he would not go that far but urged the mayor to look carefully at the damage he has done to the office of the mayor and the council.
Mr Brown planned to address councillors about his personal situation at the first, informal meeting of the new council on Tuesday.
Mr Brown's chief of staff, Phil Wilson, said he had been advised that there was nothing in legislation, standing orders or the council code of conduct that obliges the mayor or any councillor to make a formal statement about personal behaviour.
"Of course Len is addressing all councillors individually and we have the full governing body meeting informally on Tuesday and he will address them at that time," Mr Wilson said.
Last night, Mr Brown decided not to attend the youth development annual excellence awards at Government House in Auckland.
One councillor said Mr Brown had betrayed the confidence of councillors and the public, "but whether it is a hanging indictment I genuinely don't know".
Auckland University employment law expert Bill Hodge told the Herald he recalled a case from the mid-2000s where an employee at the old Auckland City Council was sacked for having sex on the job.
Mr Brown is not an employee of the council, he is an elected office holder so the same rules do not apply to him - making the situation "hypocritical", said Dr Hodge.
"Prior to Len Brown becoming mayor and prior to becoming a super city [Auckland City Council] fired a security guard for a single incidence of having a sexual activity with another person on the job," he said. "It's a disparity of treatment that an employee gets fired, and did in fact, and it's even [more] ironical that it was a security guard because apparently a security guard did find them [Mr Brown and Ms Chuang] at one point."
Read more:
• Chuang: I felt pressured to reveal Brown affair
• Len Brown's daughters: 'We stand by Dad'