The council agency had said opening the tunnels with just one station - possibly near Aotea Square - to be followed by two others as funding and passenger demand dictates was among various options under study.
But a spokesman for Mr Brown said that although it was appropriate for the organisation to consider options, "the mayor does not support any proposal for staging".
That followed an earlier mayoral statement that the project would cost $2.86 billion but with no impact on rates until after its completion, as long as that could be achieved by 2021.
Delaying that by three years - before which Britomart would reach capacity unless turned into an open-ended station - would push the cost to $3.2 billion.
Mr Brown said there was no solution for Auckland's transport woes that did not involve the tunnels project.
"It is our single biggest transformer for the region and its economic growth."
He said support for the project came from the visiting deputy chairman of Transport for London, Daniel Moylan, who told him the most important thing that city had done for itself and Britain's economy was to invest in its rail network.
But Mr Brown said Auckland Transport's search for the most efficient option would not mean accepting sub-optimal, piecemeal proposals.
"Auckland deserves better than that - a cheap compromise for the harbour bridge ended up costing us much more than would otherwise have been the case and causing as many problems as it solved."
The mayor's spokesman said the $3.2 billion estimate for a delayed project came from Auckland Transport.
But council transport chairman Mike Lee, who is also an Auckland Transport board member, said the real price for the tunnels, stations and land was $1.9 billion in non-inflated dollars. He believed that could be brought below $1.5 billion through a competitive, international tendering process.
Auckland Transport has estimated the cost of construction and land purchases at $2.03 billion in 2012 dollars, but has indicated a potential saving of $166 million.