Mr Brown, who is a nonsmoker, said the matter was being considered by Auckland's 21 local boards and he looked forward to their thoughts.
"Smokefree policies, whether in specified areas or for events, are education and awareness focused ... They are not punitive and cannot be enforced.
"This approach relies on the public being well informed about the rationale for smokefree areas or events, and for restrictions to be clearly signposted."
The council's decision on the smokefree policy would be included in the Auckland Plan, which would be finalised by the end of March, Mr Brown said.
By 7pm yesterday, more than 11,500 people had answered an online poll on the Herald website, with the overwhelming majority supporting the ban. Forty-three per cent said the ban was an "excellent and sensible idea" and 27 per cent believed it was a "good idea in theory".
Four per cent of those who answered said they were not a fan "but would go along with it". Just over a quarter said the proposed ban was "outrageous" and "a step too far".
Of the six Auckland councillors the Herald contacted yesterday, three said they supported the ban.
George Wood said a key aim of the Auckland Plan was to put children first and improve their health and wellbeing.
"So we get the outline of the commitment in the Auckland Plan will be a great first start/stage of this initiative. We would then work through the detail of how we will lessen the impact of second-hand smoke in public areas. It is people blowing their smoke over other people that must be reduced as those other people include children."
Auckland councillor Calum Penrose, a nonsmoker, agreed with those who said the proposal was outrageous.
"[It's] absolute rubbish and [I] don't support it and I am a nonsmoker. Next we will be telling people when they can and cannot go to the toilet."
Councillor Sandra Coney supported a smokefree policy, but said she would never support voting "to start putting up signs everywhere and bylaws to stop lighting up a cigarette in Aotea Square".
"My approach is not to be the heavy-handed policeman but incrementally to encourage people to not to smoke."