Prime Minister John Key is holding out hope of a change of national flag, despite strong support for the status quo.
Labour leader Andrew Little, on the other hand, says the flag issue can be addressed again when New Zealand considers becoming a Republic.
Voting on the second flag referendum is now at the half-way point.
Mr Key, who has voted for an alternative flag, said this morning he remained optimistic that the flag would change.
"I hang around in the wrong circles obviously because the wrong people keep telling me they've all voted for change," he told reporters.
"There must be a lot of people voting for change the other way because the polls tell you that. But let's see how it goes."
Mr Key also addressed criticism of the referendum's cost. He highlighted reports in Australia that a referendum on same-sex marriage there would cost A$520 million ($585 million).
"When people say $26 million is a lot - it is an awful lot of money and I appreciate that - but I think that it's a debate that's been worth having."
Mr Little said he had voted to retain the existing flag.
"I don't think the new flag that has been put up at all represents New Zealand," he said. "It is not representative of our Maori heritage at all. And I just think if we do end up adopting that flag, we will have that flag for a long time to come. And I think we can do better."
He would not say whether a Labour Government would revisit the issue of a flag change. But he expected it to come up when Queen Elizabeth II died.
Mr Little said he had not considered constitutional changes in Labour's first term of Government. But he was personally in favour of a written constitution.
"I think in this day and age every citizen is entitled to have a place that they can go to to see what their rights are as against the state and to understand the state's powers."
Voting in the second flag referendum is set to surpass the first referendum. As of yesterday, the Electoral Commission had received 1,406,070 voting papers.
The total number of votes in the first referendum was 1,546,734, or 48 per cent of eligible voters. At the same point in the first referendum, around 800,000 votes had been received.
The last referendum on a constitutional issue, the MMP vote in 2011, had a turnout of 2,257,243 people (73 per cent of the voting population), though it was held during a general election.