Prime Minister Jacinda Ardern is "frustrated" that RNZ pushed ahead with announcing proposed changes to its Concert radio station.
RNZ is planning to take the classical music station off the FM frequency and replace it with a new station aimed at reaching a wider, younger audience.
Jacinda Ardern told Morning Report the government had asked for time to find an alternative.
"I feel very strongly about this. When I came in as Minister for Arts, Culture and Heritage, one of the priorities I had was access - that we need to broaden the access of all New Zealander to the arts," she said.
"I understand that RNZ has obligations to all New Zealanders, and it is their view that they are not catering for one sector. But it is my view as arts minister that one does not need to come at the cost of another.
"My frustration here is that I see this beyond a programming decision and into a structural decision."
She said when Broadcasting Minister Kris Faafoi was briefed - very recently - on some of the proposed changes, he expressed concern and one of his clear concerns was over the loss of FM frequency for Concert.
"He explicitly asked for time so that we could see if whether or not there was something we could do to prevent the loss of the FM frequency for Concert. RNZ went ahead and announced this regardless."
Broadening access, increasing what young people can hear should not come at the cost of what others hear, she said.
Cabinet will discuss the move today.
"We tried to and asked for some time to explore and investigate how we could make sure that this wasn't an outcome that RNZ subsequently announced anyway.
"I'm pretty frustrated by that situation. It's unacceptable."
An additional $10 million has gone into Radio New Zealand under this government, Ardern said.
"So, we of course support public broadcasting."
She said the government supported RNZ's obligations to reach a wider audience and also accepted that that wasn't necessarily the case currently.
"We are going to keep going with our plans to see if there are alternatives.
"This is not cutting one generation after another or one audience after another. We don't have to lose one for the other."
More than 10,000 people have signed a petition calling on RNZ to ditch plans to gut its music station Concert.
In the biggest overhaul of its music services in years, RNZ is proposing to remove Concert from its FM frequencies and transform it into an automated nonstop music station which will stream online and play on AM radio.
It would be replaced on FM by a service aimed at a younger, more diverse audience as part of a new multimedia "music brand".
Concert would be taken off FM radio on 29 May and the youth platform would be phased in ahead of its full launch on 28 August.
The move would eliminate 17 jobs at RNZ Music, including all Concert presenter roles, from late March.
Former Prime Minister Helen Clark also added to the chorus of concern on Twitter.
She said the marginalisation of RNZ Concert equated to a dumbing down of cultural life in New Zealand.