Green leader James Shaw said supporting a members' bill on it in the next term would depend on the nature of the bill, and was "too hypothetical to answer". "We might have solved it by then anyway."
Because National has 56 MPs, it can use the members' bill process to get laws passed with support from either NZ First or the Green Party. That means it could mount members bills on issues that either of those parties approve of embarrass Labour or force it to veto a bill. It can also pass bills on its own if NZ First abstains - or with Act's David Seymour if the Green Party abstains.
Under the former National Government, Labour could only do the same if it could get both United Future and the Maori Party on board as well as the Greens and NZ First. That happened on only a couple of occasions, such as Labour's members' bill to extend paid parental leave to 26 weeks.
The Kermadecs sanctuary is understood to be mentioned in the Green Party's agreement with Labour, which will be released along with NZ First's on Tuesday.
Green Party leader James Shaw and NZ First leader Winston Peters both rejected a Sunday Star Times report that the Kermadec Ocean Sanctuary was one of the casualties of the negotiations and that Labour had agreed with NZ First not to move on it the first term.
Shaw said the report was incorrect and while there were issues still to be working through in terms of consultation with Maori over fishing quota and cultural take rights, he expected progress on it, possibly in the first term. It is understood the sanctuary is mentioned in the Green Party's agreement with Labour.
Ardern is spending the weekend sorting out which ministers will get which portfolios, including talking with Peters over the NZ First ministers.
Posts understood to be likely to be allocated to NZ First include regional development, forestry, defence, State Owned Enterprises, and an associate finance role. Foreign Affairs could also be handed back to Peters or Shane Jones and Peters will decide on the offer of deputy Prime Minister. Tourism could go to Fletcher Tabuteau.
Another issue which could cause some conflict in the positions of the governing parties is on future block offers for mining permits.
On TVNZ's The Nation, Ardern said Labour would start to wind back the block offer permits and the next round could be the last.
NZ First is more supportive of the mining industry as part of regional development and jobs and it is likely either Winston Peters or Shane Jones will get a new Regional Development portfolio when the ministerial posts are handed out.