Deputy Prime Minister Grant Robertson wants the Government to bring forward work on a second Waitematā crossing, likely to be a tunnel.
It is understood that the Government is also considering scrapping its $785 million walking and cycling bridge over the harbour.
On Tuesday, Robertson would not confirm that the walking and cycling bridge would definitely be going ahead, only that the bridge was the current proposal.
When asked whether he would renege on building the bridge, Robertson said "we continually look at the network and the programme to make sure that it works well".
"We do want to find ways of connecting the North Shore and the isthmus for people on all different modes of transport - the exact way we do that, we've come up with a proposal, and we're working that through."
Robertson would not say whether the bridge would definitely happen, however it was the current proposal.
"That is the proposal we are working on," he said.
The bridge has come under severe criticism since it was announced in June. Criticism has focused on its poor value for money and the fact it was announced at the same time as the Government scrapped a host of expensive roads.
Robertson said he wanted a solution that treated all modes fairly. The current plan for the bridge only serves two modes - walking and cycling. Private vehicles and public transport are not included.
"What I'm saying is it is a transport network - we need to make sure that all modes get a fair go."
He said his personal view was the Government was not talking enough about the work it was doing on the other Auckland harbour crossing, likely to be a tunnel under the harbour.
Robertson said that "work is under way on the so-called second harbour crossing", and the Government was doing the "planning and work and looking at the geotechnical issues around that".
"I believe it is something that if we can bring forward, we should."
The construction on that crossing, which should cost more than $10b, is not scheduled to begin until the 2030s. It could include a rail line and space for private vehicles, although just what the tunnel would carry has not been decided.
National campaigned on bringing forward a second harbour crossing at the last election.
Leader Judith Collins agreed it should be brought forward.
"It's all about whether or not we have another bridge or a tunnel," she said.
"The tunnel is an optimal solution.
"We're not in government at the moment, but I can tell you we will not fund, nor will we deliver on a cycle bridge over the Waitematā Harbour."