"Whole communities have been blindsided by these changes and councillors have become no more than mere spectators to these across-the-board changes," he said.
Mr Brown has rejected Mr Quax's motion on the grounds it is "not related to the role or functions of the governing body".
He said the governing body did not have the legal ability to accept late submissions to the proposed Plan, nor the ability to allow the proposed up-zoning of houses.
Mr Brown said the council was taking part in a statutory process and the legislation allowed anyone affected by "out of scope" changes to appeal to the Environment Court.
"Out of scope" changes are made by the council to its latest position on the Unitary Plan without any supporting submissions.
The proposals are causing a deep rift in the council. Nine of the 20 councillors are asking for further public input.
The councillors who signed the notice of motion are Mr Quax, George Wood, Chris Fletcher, Cameron Brewer, Denise Krum, Cathy Casey, John Watson, Mike Lee and Sharon Stewart.
The independent hearings panel for the Unitary Plan will consider the changes and make formal recommendations to the council mid next year.
The council will approve the plan in the lead-up to next October's local body elections.
Mayoral candidate and Labour MP Phil Goff said the issue needed to be handled sensitively. He said he supported intensification in the city and along arterial routes, but the council had to leave aside areas where there were strong objections to townhouses, studios and apartments of up to three storeys.
Senior council planner John Duguid has told the Herald that tens of thousands of suburban homes in Auckland would probably be rezoned from single house to multiple townhouses and apartments.
What the notice of motion said:
"That the Auckland Council should not seek to allow the up-zoning of residential properties without first undertaking full public consultation with the Auckland community so as to facilitate good faith and natural justice with affected property owners."
What councillors say:
Monday, December 14, 2015 3:18 p.m.
"I am very concerned at the many recent zoning changes, which have been made without the public's knowledge or permission. The Notice of Motion was a way of letting the public back into the process and I am disappointed that we are not going to have that debate. I feel the public has been shut out of this very important process that is reshaping Auckland into the future."
- Cr Cathy Casey
"This request to allow public input, even at this late stage, will allow communities to express their views. The Local Government Act expressly states that councillors must know the views of their communities before making decisions. Justice has been swept aside in an endeavour to satisfy the Government timeline. Auckland Council should stand up far stronger."
- Cr George Wood
" Auckland Council continues to mishandle the Unitary Plan process. We will likely see Auckland branded as disempowered rather than empowered communities."
- Cr Chris Fletcher
"I'm very disappointed in the response of the Mayor that he has decided not to let us discuss this at the Governing body meeting on Thursday? This is one of the most important issues for our communities."
- Cr Sharon Stewart
"Before the last local body elections, the council watered down its intensification plans following huge public outrage. To think it's now systematically strengthening those provisions again and in complete secret is a huge insult to democracy and the public. At the very least the Mayor needs to give this notice of motion a fair hearing. To dismiss it absolutely outright just shows how removed and undemocratic the process has become."
- Cr Cameron Brewer