Transport Minister Stephen Joyce says Auckland's next harbour crossing is likely to be a toll road.
The Transport Agency released a report on Monday saying a bridge would be cheaper, but the Government hasn't yet decided which option it will back.
The report said a new bridge would cost about $3.9 billion, while a tunnel crossing would cost about $5.3 billion.
Mr Joyce says the project is large, and will have to be funded by taxpayers, ratepayers and by tolls on users.
A public transport group says any plans for a new harbour crossing in Auckland should start with rail tunnels.
The Transport Agency report said the cost of rail tracks is hard to justify because the Northern Busway, which links the North Shore with the City, is expected to cater for passengers for the next 30 years.
However the spokesperson for the Campaign for Better Transport, Cameron Pitches, says the Government should push ahead with rail tunnels regardless of whether it does the same for vehicle traffic later.
Mr Pitches says rail is more efficient, because one line can carry the same number of people as ten motorway lanes full of traffic.
Traffic on the Auckland Harbour bridge - currently 168,000 vehicles a day - is expected to rise by about 40,000 vehicles a day by 2041.
The Government wants a new crossing built in the next 20 years to cope with demand.