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The response nearly mirrored a TVNZ Colmar Brunton poll showing 79 per cent of respondents were against the policy.
Ian Leckie, of the NZ Educational Alliance Institute, which has united with several other key sector groups to fight the plan, was not surprised by the survey results.
"What we are saying - and this survey backs it up - is that there is a very high level of support for the stand that the sector group has taken," he said.
"The message for the Government is that this does not have broad public support and doesn't have any sector support."
He called on the Government to re-think the policy.
New Zealand Principals Federation president Paul Drummond said the survey result was consistent with "overwhelming anecdotal evidence" that the policy was opposed by most Kiwis.
"I'm hoping the Government doesn't paint itself so far in a corner that it doesn't find a compromise."
Secondary Principals' Association of New Zealand president Patrick Walsh said feedback principals had received across the country showed a universal opposition.
"Many of them are flabbergasted the Government could ever think this was a good idea," Mr Walsh said.
"I'm surprised they haven't listened. When you get an unprecedented alliance of teacher unions, principals' groups, and school trustees, backed up by public and parents' opinion, any politician worth their salt needs to take that into account. A trade-off between quality and quantity is just a really bad concept. The most precious thing to parents and the New Zealand public is their children's education. When you increase class sizes and start compromising that, well that is what has caused the outrage up and down the country."
Mrs Parata was not immediately available for comment, but Labour and the Green Party echoed their views in fresh attacks.
Labour's education spokesperson Nanaia Mahuta said: "The Government is trying to convince mums and dads that trade-offs - either larger classes or quality teaching - are necessary.
"Parents are not stupid.
"The minister would be better off reversing her decision and engaging constructively with the sector to come up with workable and informed solutions to improve educational outcomes for all our children."
Green Party education spokesperson Catherine Delahunty called on the minister to order private schools to also increase their class sizes.
"By allowing these schools to keep their student teacher ratios low, the Government is effectively subsidising lower class sizes for wealthy children. As underprivileged children struggle in classes of nearly 30 pupils, wealthy kids have their class sizes capped at half that. That is blatantly unfair."
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