"The agency should be working quickly with Auckland Transport to progress a road and rail crossing, and look at a rail-only crossing."
The poll asked about people's support for a road-only crossing, a road and rail crossing and a rail-only crossing.
An Auckland harbour crossing for rail and road was the most popular. Almost two thirds (64 per cent) said they would support that option.
The option with the second highest level of support was a rail-only crossing, backed by 42 per cent; 29 per cent had a neutral opinion and 29 per cent opposed it.
The research also found support for the rail and road crossing was generally higher among "wealthier and older respondents".
Mr Beckett said the Government and Auckland Transport must work together to ensure planning for a combined road and rail crossing was progressed at the same time.
"After the City Rail Link is built the next major area of development is the North Shore."
Mr Beckett believed documents from the New Zealand Transport Agency released to the Transport Blog in May showed the Government only planned to designate for a road-based crossing.
In a paper by the Transport Agency from November 2014, one of the key issues was that there was no rail on the North Shore so Auckland Transport's support for protecting the route for rail "now is unclear".
However, a briefing document three months later said the business case, to be completed next year, would consider rapid transit options.
Transport Minister Simon Bridges said suggestions the NZTA were focused on a road-only solution for a future tunnel across Auckland's Waitemata Harbour were "misleading and inaccurate".
The Transport Agency and Auckland Transport were working together to ensure a future crossing delivered a multi-modal transport solution by providing more options for moving people and freight across the harbour while supporting growth and resilience, Mr Bridges said.
"While the Government hasn't yet decided when it will be required, and precisely what form it will take, in a rapidly growing region it's essential that we protect and keep future transport options open."
The NZTA can only designate for the road component of the crossing and so is working with Auckland Transport to ensure any designation was future-proofed and enabled a rapid transit and public transport crossing, Mr Bridges said.