New Zealand's vote against changing the flag shows that a potential shift to a republic is a long way off, Deputy Prime Minister Bill English says.

After voters chose to retain the national flag in a referendum last week, attention has turned to the next opportunity to debate New Zealand's national identity or constitutional arrangements.

Both major political parties said this morning that a debate on becoming a republic was not a priority.

Mr English told reporters at Parliament: "For most people they've had a vigorous debate, they've confirmed the current flag, and I hope people embrace the current flag, use it more, be enthusiastic about it.

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"I think it will be some time before there's any change in either the flag or some push for republicanism."

Mr English also showed no interest in allowing New Zealanders to elect their head of state.

He was "very happy" with the process for appointing a Governor-General, and did not expect a public debate about it.

"Whatever happens with the royalty in Britain, it looks pretty well-embedded," he said.

"And I think the recent vote on the flag shows that New Zealanders are reluctant to change something if they think it's working."

At present, the Prime Minister appoints the Governor-General. After the appointment of Dame Patsy Reddy to the role last week, Green Party co-leader Metiria Turei said the election of a head of state should require the support of 75 per cent of Parliament.

Labour leader Andrew Little reiterated this morning that New Zealanders should have been given the option to vote on whether they wanted to change the flag. The Government "did not extend any courtesy to them as citizens", he said.

"The flag debate showed that New Zealanders weren't prepared ... or perhaps hadn't had the case made to them that we should make that sort of change.

"And that in the end goes to leadership, and we simply didn't have it on the flag stuff."

Mr Little wanted a discussion about becoming a republic, but said it was not a top priority for Labour.

A constitutional debate would likely be "triggered by events", he said - most likely the death of Queen Elizabeth II.