It says smaller rail tunnels would cost a quarter as much, leaving plenty of money to extend tracks right up the North Shore.
Campaign convener Cameron Pitches has, in a letter to Transport Minister Simon Bridges, accused the agency of failing to consult Aucklanders about its preferred crossing, and asking him to intervene to stop a route protection contract being awarded early next month. "There is no point in protecting a route for a mode of transport that may prove to be of little value in the future," he said.
He has also written to Auckland Mayor Len Brown and councillors, warning them that $4 billion will not pay for increasing the capacity of the surrounding motorway network.
Mr Bridges said last night rail had not been ruled out, and he had been assured "that proper process and consultation has been followed".
Agency northern director Ernst Zollner said the public had been consulted through the project's identification in the 2012 Auckland Plan, and would continue to be kept in the loop through a designation hearing and development of a business case.
"A business case will determine when the crossing is needed, and what modes of transport it will include.
"The project is not at that stage yet, and suggestions that decisions about its form have already been made are inaccurate and misleading."
The agency has earmarked about $15 million for the business case, with a reserve allocation of around $10 million for property purchases should it decide to build a crossing. Its industry presentation depicted double-deck tunnels with three motorway lanes on top and rail below, which it said would cost "around $4 billion". That compares with rail-only tunnels estimated in 2008 at $1 billion to $1.2 billion.
But in March, Mr Bridges, said the main project was likely to cost between $4 billion and $6 billion.
Mr Brown would not be drawn on the campaigners' preference, saying the project needed to be prioritised in relation to other vital transport infrastructure for the city, as well as ensuring it was future-proofed for rail. "That's why agreement with the Government on an Auckland transport accord is so important."
Another harbour crossing by 2030
• Government's preference: Twin tunnels, each with three motorway lanes with potential for trains to run underneath - expected to cost $4bn to $6bn.
• Campaigners' preference: Smaller rail-only tunnels estimated in 2008 at $1bn to $1.2bn.