Labour apears to be inching closer towards republicanism, with delegates at its annual conference in Christchurch giving the green light to a proposal to hold a binding referendum on whether to ditch the monarchy on the death of the Queen.

At yesterday's conference the party agreed to send a remit on the proposal from prospective Wairarapa candidate Kieran McAnulty, who is also treasurer of the Republican Movement, to a full vote from delegates today. Sources say it is likely to pass without dissent.

The move comes as a new poll shows a small majority of New Zealanders are in favour of such a referendum.

The Republican Movement poll, conducted by pollsters Curia, showed 47 per cent of New Zealanders supported the idea of a referendum on the Queen's death, with 44 per cent against and 9 per cent uncertain.

A poll in June on support for a republic found 40 per cent support to 53 per cent against.

Labour leader David Cunliffe refused to say whether he supported a referendum, saying his personal position "is not actually that relevant".

He added: "What Labour supports is to have a constitutional conversation which will allow all New Zealanders to think about how we might evolve our constitution over time."

But Cunliffe singled out the royals in his first speech to Labour's conference since being elected leader, accusing the Government of snubbing a convention that invitations were not issued for a royal visit during an election year. Recent polls indicate the party could form a government this time next year - with the help of the Greens.

Cunliffe said Prime Minister John Key would invite the royal family to bring "its newest and cutest member here for a long series of photo ops in an election year", referring to Prince William, wife Kate and their baby George.

"They should come. But will John Key dare take the Duke and Duchess back to McGehan Close? Will he take them to a closed sawmill in Rotorua or a boarded-up tannery in Shannon?"

The Republican Movement's poll found Green and Labour voters were more likely to be in favour of a referendum, but 42 per cent of National voters also favoured a vote over who was our head of state.

Movement chairman Lewis Holden said the result clearly showed New Zealanders wanted a say on the controversial subject, whatever their MPs thought.

The monarchy had been assisted recently because Prince William and Kate had been treated as celebrities, Holden said. This divorced them from their constitutional role and turned them into a "high-class version of the Kardashians", he added.

Monarchy NZ chairman Sean Palmer said the poll results ran counter to other recent polls, with the latest demonstrating the republicans' "growing irrelevance", and said they were now twisting their questions to get the response they wanted.

"It seems republicanism is so unpopular at the moment that the only way republicans can get any traction at all is if they completely remove the current Queen from the equation.

"As even that question is not giving them the answer they would like, they have managed to construct an even more oblique one. They are now asking people if they should be asking people a question."

Former Deputy Secretary of Foreign Affairs and Trade Peter Hamilton told the Republican Movement's annual conference, also in Christchurch, that having the Queen as head of state was holding New Zealand back.