Chris Hipkins has admitted Labour made a "mistake" with the entrenchment clause in its Three Waters legislation.
The Leader of the House announced the government would fix the Water Services Entities Bill this week by removing the entrenchment clause that was voted on during committee stages.
The provision in Three Waters legislation would make it more difficult to privatise water assets.
Hipkins said it was a "mistake" to put the clause in.
"The intention to protect assets from being sold was right, but entrenchment usually requires a super majority or 75 percent of the Parliament to vote for it," he said.
He told RNZ although this was initially proposed there was not the support across the House for it.
The Greens then put forward an amendment suggesting a 60 percent majority be required to make an amendment, he said.
"At that point, Labour should have withdrawn its support. We didn't."
Hipkins said they now had to "acknowledge that was a mistake" and fix it before the bill's third reading.
National's Shadow Leader of the House Chris Bishop said the government and the Greens were caught out trying to make the unpopular Three Waters legislation harder to overturn.
"Entrenchment is a rarely-used provision that, until now, has been reserved for important constitutional matters and legal experts say its use in this case is deeply inappropriate," Bishop said.
He also called into question the prime minister's claims she was unaware of the bill amendment.
"Prime Minister Jacinda Ardern said she was unaware the bill had been amended, however Local Government Minister Nanaia Mahuta later admitted it was discussed in caucus - which the prime minister chairs."
Bishop said the bill was a shambles and "National would repeal and replace the Three Waters bill and ensure water assets remain with local authorities" if elected.
ACT leader David Seymour said the removal of the entrenchment was "a win for democracy" but "the Government's intentions remain concerning."
"This entire process has been deliberately murky and questions remain about how it even got to this point," he said in a statement.
Seymour said "the Greens and Labour have been grossly irresponsible, not realising what they are doing to New Zealand's constitutional framework while trying to fight the imaginary bogeyman of privatisation".
It follows earlier in the week when Local Government Minister Nanaia Mahuta told the House that while it "may not pass the constitutional threshold, there is a moral obligation of people who believe that privatisation should not occur to support that particular [clause]".
Hipkins acknowledged that the approach in this amendment "allowed an entrenchment provision to pass in a way that is not typical for Parliament".
He said that had wider ramifications that "they were not comfortable with".
But he said by putting the bill back with the committee before its third reading, they had the opportunity to fix it "before any constitutional precedent has been established".
Meanwhile the Greens have defended their stance.
"Requiring a 60 percent majority of Parliament, or a straight majority in a referendum, would require any future government to build political support and consensus for any winding back of public ownership. This would uphold the very strong public support for public ownership by preventing a simple majority changing the law to privatise precious water assets," Green Party local government spokesperson Eugenie Sage said in a statement.
"Parliament's Standing Orders (270) clearly provide for entrenchment and that Parliament must carry any entrenchment proposal by the same majority as in the entrenchment clause. That's what happened with the Greens amendment," she said.
The Green Party would continue to fight for strong protection of the ongoing public ownership of the three waters assets, services and infrastructure, Sage said.
The party was disappointed at how the debate unfolded and it showed an urgent need for a public conversation about how to better protect core public assets, she said.