Negotiations between the Government and Māori over the proposed Kermadec ocean sanctuary are continuing, but the Prime Minister has already ruled out a cash settlement.
The Māori Fisheries Trust, or Te Ohu Kaimoana, is contesting what would be a 620,000 square kilometres in the northeastern corner of New Zealand's exclusive economic zone.
It says a Treaty of Waitangi settlement gives iwi fishing rights in the area, and in March announced court action.
The group was meant to hold a news conference at 5pm on Monday with the outcome of discussions with the Government, but that was postponed until at least Tuesday as talks continue.
Prime Minister John Key says the parties are at somewhat of an impasse.
"At the core of their belief, they believe they should be entitled to fish there even though they haven't; they believe they should. We believe it should be a sanctuary where they shouldn't fish.
"You've got a slightly unusual situation because iwi when it comes to conservation issues and conservation groups are [usually] on the same page. On this one they're on the completely different page and they just don't agree."
At his post-Cabinet news conference before the scheduled news conference on Monday afternoon, Mr Key said the Government's preference was to pass the legislation and appeared to have the numbers to do so with the Green Party's support.
"We have absolutely no intentions of backing off it being a sanctuary.
"Personally, I think it's a bit of a moot debate about fishing out there because it's a very long way away where people have historically not been doing much and the quota that was out there was tiny. I don't think it's been fished in for the last decade."
He ruled out any kind of cash deal with the group, but said "at the margin there might be one or two little things" that could be compromised.
The Government believes the species of fish in the proposed sanctuary are migratory so iwi will still be able to catch them outside the boundaries.
There's been a big push to increase the amount of protected ocean recently, including at this year's World Conservation Congress in Hawaii, which took place between September 1 and 10.
During the conference, attended by thousands of government officials, the International Union for Conservation of Nature voted to support increasing the portion of protected ocean to 30 percent by 2030.
In late August, United States President Barack Obama announced the expansion of the Papahānaumokuākea Marine National Monument off the coast of Hawaii, making it the biggest in the world.
Created in 2006 by President George W Bush, it gained UNESCO World Heritage Site status in 2010. The expansion increases its size from 1,146,798 square kilometres to 1,508,870 square kilometres of protected area, which makes it twice the size of Texas.