Half of Kiwis would see a return by the United States Navy to New Zealand ports as a positive move but a large minority don't want their ships back, shows the latest Herald DigiPoll survey.
Prime Minister John Key believes resuming ship visits would be a positive step and extend markedly improved relations between the nations.
"Most New Zealanders can see the relationship with the United States has dramatically improved in recent times," he told the Herald. "A ship visit that is within NZ law would be a positive step."
A total 29.4 per cent don't want a ship to visit at all; 50.2 per cent think it would be a positive move; and 16 per cent displayed a sense of triumphalism by preferring to think it would be a victory for New Zealand's anti-nuclear policy.
The Navy has invited the US Navy, among others in the world, to its 75th birthday celebrations in November and the Pentagon is considering it.
But an acceptance would run counter to the most significant remaining reprisal against New Zealand's anti-nuclear laws.
The US Navy has boycotted NZ ports since 1986 when New Zealand was effectively expelled from the Anzus security pact with the US and Australia.
Reprisals have eased only in recent years. The ban on the US exercising with NZ was lifted only in 2010. But even then the Kiwis were not allowed to dock in naval facilities at Pearl Harbour but had to dock at a civilian wharf. President Barack Obama overturned that particular oddity for the 2014 Rimpac exercise.
Under New Zealand law, ships may visit only if the Prime Minister is satisfied they are not carrying nuclear weapons.
It does not require any confirmation that a ship is not nuclear armed but the US has always considered a visit by one of its ships would breach its policy of neither confirming nor denying whether its ships are nuclear armed.
Labour leader Andrew Little said the 50.2 per cent confirmed that people wanted NZ to have a good relationship with the US. "It is important that we do have a good relationship with them. But what is equally important to New Zealanders is our non-nuclear status. It has defined us as a nation for the past 30 years."
Mr Little believed the almost 30 per cent who did not want the US to visit would be those who, despite any assurances from the Prime Minister, would have doubts about whether any visiting US ship was actually non-nuclear.
He said the three options were not exclusive and there might be people who thought a ship visit was positive, but might doubt an assurance.
US ambassador Mark Gilbert was not available for comment but an embassy spokesperson emphasised other areas of co-operation.
"No decision has been made yet. Our bilateral military co-operation is strong, and we continue to partner in humanitarian assistance, disaster relief and peacekeeping support operations. Our relationship with New Zealand ... continues to grow, and we discuss and co-operate on a wide range of issues at the highest levels."