The newly-established Iwi Education Authority says it would support league tables for schools.
Prime Minister John Key says it is a good way for parents to get information on how schools are performing.
He says it makes sense to introduce them for primary schools, using national standards data.
The Iwi Education Authority, which represents 23 kura, says it backs the tables because schools would be more accountable for performance and responsible for achieving results.
Chair of the tribal body Pem Bird says if league tables are about making the performance of a kura public, he does not mind at all.
The union representing primary school teachers, however, says the Government has been misinformed about the benefits of league tables and introducing them would be a terrible idea.
New Zealand Educational Institute president Ian Leckie told Morning Report it would be totally destructive to education to make league tables out of national standards.
"To rank schools on a narrow measure really means schools will narrow their curriculum to the measures that are seen to be successful and that's not a step forward for New Zealand education.
"That's why the political view is just so far out of kilter with what's good for children."
He says the tables would create the wrong picture of school quality, and the Government should keep that information out of the public domain.
Secondary Principals' Association President Patrick Walsh agrees league tables would ultimately lead to a narrower curriculum.
He says the association is happy to discuss quality teaching with the Minister of Education and the Ministry of Education but objects to on-the-hoof announcements being made without any research or consultation.
Listen to NZEI president Ian Leckie
Parents 'hungry for information'
Independent think-tank the New Zealand Initiative says introducing league tables to primary schools could help improve the country's education system.
Co-chair Roger Partridge says any tables would have to be carefully thought through, but would at least give an indication of a school's performance.
He says parents are hungry for that information so they can make informed decisions about where to send their children to school.
However the principal of Paparoa Street School in Christchurch, Phil Harding, says a league table would force schools to focus on producing good data rather than good students.
He says the risk is that schools will focus entirely on reading, writing and maths at the expense of other important subjects.
Mr Harding says parents will unfairly judge schools when the results are not comparable.
And University of Otago education professor Alison Gilmore told Nine to Noon overseas experience has shown that league tables have negative consequences for schools.
Listen to full interview on Nine to Noon