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That will leave Labour reliant on the National Party to stick to its pledge to support the legislation needed to implement the agreement once it is signed.
Ardern confirmed Labour is set to sign up for the revised verstion of the Trans Pacific Partnership after changes during last-minute negotiations on the sidelines of Apec in Vietnam.
Legislation to introduce the agreement - now renamed CPTPP (Comprehensive, Progressive Trans Pacific Partnership) - would go to Parliament including a select committee process to ensure there could be public input.
Those changes included some exemptions from investor-state disputes resolution mechanisms and suspension of aspects of the agreement which were specific to the United States prior to its withdrawal.
Although Ardern said it was a marked improvement on the deal the National Government had negotiated, Green Party trade spokeswoman Golriz Ghahraman said it did not go far enough to secure the party's support.
"We don't think the changes make enough substantive difference. We are glad Pharmac is more protected but actually we can still be sued for breaches under the investment chapter so we don't think that's gone far enough."
She said it would have been good if New Zealand had pushed harder, as Canada and Vietnam had done. She said Labour had always known the Greens would oppose it and it was made clear in negotiations before it signed up for its confidence and supply agreement. It would not impact on the Government's ability to sign up to the CPTPP.
National leader Bill English has promised National's support to get the deal done, saying it was vitally important for the country and wider region.
The Greens will also seek a change in the processes to ensure no further trade agreements could be entered without Parliamentary scrutiny and approval.
"[Former US President] Barack Obama introduced legislation that bound the American executive on human rights and environmental and democracy issues. I would like to talk to the Government and look into introducing law to make sure we don't have this kind of trade agreement come up again in future."
She said that would mean such agreements had to enforce the social responsibilities of multinationals, and ensure the protection of human rights and environmental issues.
There are still some negotiations to be held before the CPTPP is finally agreed on, but local business groups and exporters welcomed the news it was still a viable option.
BusinessNZ chief executive Kirk Hope said a successful conclusion would mean more jobs and more exports and help insulate New Zealand against any economic shocks.
"Every extra billion dollars in exports equates to 8,500 new jobs, but New Zealand has not yet achieved many trade agreements - only 8, with 16 countries, far fewer than many other comparable countries have."
Kim Campbell, the chief executive of the Employers' and Manufacturers' Association, said it would be to New Zealand's advantage and give access to markets such as Japan.
"The CPTPP gives New Zealand access to some of our most significant trading partners, along with opening other doors. While it's not perfect, it has to be the way forward."