A new law would empower the Education Minister to impose extra conditions on any Government money given to schools in exchange for ditching parent donations.
But the National Party says the Government is being "undemocratic" for not allowing select committee scrutiny of the proposed ministerial powers.
The education and workforce select committee has reported back on the Education (School Donations) Amendment bill, recommending it be passed without any substantive changes.
The bill would enable the Government to follow through with its Budget 2019 announcement to give $150 per student to every decile 1 to 7 schools that axed parent donations.
The intent of the policy was widely lauded, but primary teachers' union NZEI and many schools have questioned whether it would be worth taking up the offer, given how much schools already rely on donations.
Principals have also questioned what kind of parent donations they could still seek and still be eligible for the Government grant.
That has led Education Minister Chris Hipkins to say that there would be an exception for parent donations for school camps.
Hipkins intends to add a clause to the bill during its committee stage that would empower the minister to add exemptions.
National's education spokeswoman Nikki Kaye has described this as a "very wide power", though Hipkins has said the only planned exemption at the moment is for school camps.
The select committee report added that the Education Minister should be able to determine any extra conditions around the policy, as long as school boards are made aware by a notice in the Gazette.
In its minority report on the bill, the National Party said the minister changing the bill at the committee stage was "unnecessary and undemocratic" as it bypassed select committee scrutiny.
"There are real concerns about other outdoor activities and other activities such as music lessons whereby there may be a debate as to whether they are core curriculum."
Hipkins informed the committee that bypassing the select committee was about timing, and doing so would allow the exemption for camps to be included in guidelines that were issued to schools before the committee reported back on the bill.
He has previously said that the select committee had already heard submissions by the time he decided that he wanted to amend the bill.
"Select committees don't double consult. They don't consult on the bill, make amendments, and then consult on the bill again."
National further criticised the bill, saying a "donations police" would be set up monitor compliance, and that excluding decile 8 to 10 schools would create greater inequity.
"We know that significant numbers of disadvantaged children attend these schools."
Hipkins has said that all schools could eventually be included in the scheme.