National leader Christopher Luxon expects New Zealand to become a republic but says it would not happen "in my Government and in my time".
Luxon described himself as "a soft republican" and he believes ultimately New Zealand will become a republic.
But he said the issue was not a priority and no member of the public had raised it with him since he became leader last November.
"The bottom line is there has to be a burning platform for us to discuss and open up our constitutional arrangements," he told reporters at Parliament.
"And the reality is there is just not that mood in the country at the moment.
"I don't see any need for us to change our constitutional arrangements and I don't see the New Zealand public wanting to change them."
It would be a ground-up conversation but constitutional arrangements were not what people were fixated on at present.
"Those issues are highly complex. They are a long way down the road. They are not going to change in my Government and in my time and the New Zealand people have no appetite for changing our constitutional arrangements."
Prime Minister Jacinda Ardern said while she remained of the view that New Zealand would become a republic in her lifetime she saw no need to have that conversation now. "I also intend to live a long and happy life," she told reporters at Parliament.
The death of the Queen has given rise to some questions about how much longer New Zealand remain a constitutional monarchy in which New Zealand's head of state is the monarch, King Charles III, but holds only ceremonial powers.
Ardern said there were a large number of things the Government needed to be focused on.
She believed there were a number of different views within the public.
"What I don't sense is urgency.
"While I'm sure the New Zealand public would be open-minded on the conversation at some point, I have not sensed the urgency of taking on this question right now."
Education Minister Chris Hipkins said he could be described as a "lazy republican.
"II like the idea of it but the practical reality is that the monarchy that we have at the moment is quite convenient for us. It doesn't cost very much money and actually, it works reasonably well."
Maori Crown Relations Minister Kelvin Davis said he was not concerned about whether New Zealand became a republic or not. His concern was with the Treaty of Waitangi.
"We would have to have cast-iron guarantees that Te Tiriti would not be diminished in any way if we were to become a republic."
He said it would be an interesting conversation that should be had.
"Once we've had the conversation, that's when people get to vote on it, depending on their perspective."
When asked if could be an opportunity to renegotiate the Treaty, he said "That would be quite dangerous I think."
He said the Treaty was a simple document that had become complicated. The third article, which gave Maori the same outcomes as others, was the most important.
Cabinet Minister Andrew Little said the Government should not be leading the discussion on New Zealand's constitutional arrangements. It should fall to advocacy groups.
"I don't detect a groundswell for change at the moment. Unless there is a mood for change, I don't think the system needs to respond."