A parliamentary select committee has recommended that the proposed charter schools should be subject to oversight by the Ombudsman.
The schools are based on the United States model of charter schools, where the state contracts businesses and non-profit groups to provide and run schools.
As it stands, the schools will not have to follow the national curriculum or be required to employ registered teachers, nor will they be subject to the Ombudsman's Act or the Official Information Act.
But in a report out on Friday, the education select committee has recommended that the Ombudsman's Act should apply to charter schools.
MPs have also recommended that any charter school contract should stipulate that complaints against the school be subject to independent review.
The Government intends to have the publicly-funded private schools ready to operate by the start of the next school year and will move quickly to pass legislation so the first sponsors can be selected in time to open their schools, Radio New Zealand's education correspondent says.
ACT Party leader John Banks says state schools are among the groups interested in setting up publicly-funded private schools.
Organisations representing teachers and principals say the model threatens New Zealand's system of schools governed by their local communities.
But Mr Banks, who is the Associate Minister of Education and chief proponent of charter schools, says far from being threatened, some state schools want to host the new entities in their classrooms.