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 into 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 8500 new jobs, but New Zealand has not yet achieved many trade agreements - only eight, 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."
National Party trade spokesman Todd McClay said National would continue to support it and the Green Party's stance was a shame.
"It's one of the first real trade or foreign policy tests for the new Government where they're going to get their support from going forward. I think Labour's doing the right thing, negotiating in good faith on behalf of New Zealand but it really needs to get its support partners on board for that because this is a deal that is good for New Zealand.
There's an opportunity for the whole of Parliament to come together and support trade. It would be a shame if the only way the new Government felt it could get trade deals upon the line would be to rely upon National. The point is not whether they have the numbers, because we support high quality trade agreements, but this is the first test of the new administration and they need to work hard to get the Greens and NZ First on board even though they fought so strongly against the TPP over the last nine years."
He said the position NZ First took could be interesting, given it had opposed almost every free trade agreement put before Parliament - including the China agreement when it was last in Government with Labour.
He said the changes made over the weekend were not significant, despite Ardern's claim it was much improved, and the CPTPP remained very much the same as the TPP-12.
"But with some rebranding. That's probably necessary because there was a significant amount of concern around the original deal."
He warned against celebrating too soon - saying four countries still had issues which could see it unravel.
