Some schools have enrolled as many as 50 percent more children than they have classroom space for, Education Ministry documents show.
The reports, obtained by the Labour Party under the Official Information Act, listed about 200 schools that were over capacity last year and nearly 500 others that were in danger of becoming overcrowded.
Some principals told RNZ News children were learning in libraries and computer rooms, and others warned new classrooms were bringing only temporary relief.
Several kura were near the top of the ministry's list of overcrowded schools, including Te Kura o Matapihi near Tauranga at 41 percent over capacity.
The school's tumuaki, Tui Yeager, said it was struggling to find room for its 146 students.
"We've got kids working in the library space, and it's not a big library," she said.
"We're in a computer suite and I guess we've got classes getting into bigger numbers."
Ms Yeager said the ministry wanted the school to get an enrolment scheme or cap its roll.
But she said local parents did not have any other nearby options for Māori-immersion education and the ministry needed to provide more classrooms.
"People are actually waiting to get in so we're going to end up turning families away who want Māori-medium for their children but we're not able to offer that because the ministry is so slow giving us the space or the resourcing that we need."
Other schools told RNZ News they had received new classrooms and no longer had a problem, but some expected overcrowding would soon return to dog them.
Helensville Primary School was listed as the most crowded school in Auckland at 35 percent above its classroom capacity.
Principal Deborah Heasman said things were better now, but delays in getting four new modular rooms would make things difficult later this year.
"We were expecting them at Christmas or around about that time. I have asked for some alterations which have put them back a little but at the moment we still aren't on track to get them until maybe late July, August and I've got a class I need to start and won't have a classroom for at that time."
Christchurch school's 'hands tied' on new enrolments - principal
In Christchurch, Hornby Primary School was regarded as one of the most crowded schools, at 17 percent over capacity.
Deputy principal Simon Scott said overcrowding was not an issue right now, but it would be once a rebuild of the school was complete.
"If we were to move our 243 children into the classrooms that they're providing us, it would be overcrowded," he said.
Mr Scott said the school would have to keep using three old classrooms, which the school had wanted to use for other services.
He said the ministry re-zoned the area four weeks ago in a bid to control the growth, but the school still had to turn children away.
"We've had one family who is really keen to come here, and they've tried three times, but our hands are tied," he said.
Education Ministry deputy secretary Katrina Casey said the capacity of Hornby Primary School's new buildings was agreed with the school.
Ms Casey said in July last year 50 percent of Hornby Primary School's students lived outside the area that was now the enrolment zone and only 33 percent of local Year 1-6 state school students attended the school.
She said the enrolment scheme would affect new enrolments and allow the school to reduce its student numbers to within its capacity.
Govt and Labour dispute documents' significance
Meanwhile, Education Minister Nikki Kaye said the ministry's figures published by the Labour Party were now out of date and did not take into account classrooms and buildings that had been paid for by schools' boards of trustees.
She said she was not aware of any schools where overcrowding had breached health and safety regulations.
Ms Kaye said many of the schools listed in the reports had since received new classrooms and their figures had changed.
Labour Party education spokesperson Chris Hipkins, who obtained the documents, said they showed the government had been "late to the party" in addressing critical infrastructure problems.
"They simply haven't invested enough to keep up with growing population pressures and that's why we're seeing so many more schools having to use libraries and gymnasiums as classroom spaces," he said.
Mr Hipkins said any spending in this year's government budget would not make up for years of under-investment.