A committee has been considering the scope of a study into the wider effects of the port on the city.
The Auckland development committee was due to direct council chief executive Stephen Town to begin the design of the study and its associated processes.
The broad objective of the study is to "fully investigate and report to the Auckland Council on the most effective means of meeting Auckland's import and export needs in terms of their economic, social and environmental costs and benefits".
The study - promised by Mr Brown in 2013 - comes amid a public outcry into plans by the port company to build two massive wharf extensions into Waitemata Harbour at the end of Bledisloe Wharf.
In August 2013, Mr Brown told the Herald: "Before we make any decisions about whether the port expands or otherwise, we need an informed discussion with Aucklanders, underpinned by a robust study that includes consideration of economic, social and environmental factors.
"We need to closely look at every alternative for the delivery of port services and work out what is best for Auckland."
The port company planned to begin construction this month, but had not been not ruling out a pause.
Mr Brown told TV3's The Nation programme on Saturday that he wanted "a discussion that relates to the port cooling their heels and taking a breather".
A protest movement, Stop Stealing Our Harbour, that includes prominent businessmen, boaties and public figures, attracted about 2000 people and 300 boats to a protest 10 days ago calling on the wharf extensions to be stopped immediately.
The port company has said it has abandoned an earlier plan to extend the port 250m into the harbour, but could not work miracles handling Auckland's growth without some extra room.
A report to the commitee says for the study to be credible it needs to be transparent and have meaningful input from interested parties. There should also be opportunities for the community to have a say on the study's findings.
