The Green Party is calling for an expansion of the government's one-off residence visa.
An estimated 165,000 migrant workers in New Zealand and their families are eligible if they have been here at least three years, earn more than $27 an hour or work in a job on a skills shortage list.
But the Greens' immigration spokesperson Ricardo Menéndez March said the line has been drawn clumsily as it ruled out many essential workers who were on different visas.
"If you're going to go big, get it right," he said. "This was an attempt to fix the problem that has ended up resulting in creating massive divisions within the community. We've got thousands of people who have been arbitrarily excluded.
"If the intent is to give certainty to people that are here, and also to resolve some short term issues around exploitation and backlogs, we ought to get the criteria right."
It was not too late for the government to listen to the community, he said, and the Green Party has started a petition to extend the scheme.
"Partners who would have met the criteria, who are excluded by nature of not being primary applicants, is something that needs to be fixed. People who work in essential industries as well as people who are on a student visa and have been either working full time or worked in essential industries as encouraged by the government."
Working holiday visa holders and other open work visas should be included, as well as people currently ruled out by their disabilities, he added.
While migrants who are eligible have been celebrating the government's announcement they can settle permanently within a year, others have been left ruing their luck especially those who changed to student visas or left the country just before the announcement.
Immigration New Zealand said the criteria is designed to focus on people whose primary purpose for being in New Zealand is to work, reflecting migrants' critical part in New Zealand's economy.
There were no plans to broaden eligibility criteria to include students, including PhD and masters students, it said.
Immigration Minister Kris Faafoi said in a statement on Tuesday those who do not qualify would need to explore other visa options.
"To be eligible, visa holders must have met the criteria on 29 September 2021 and remain eligible when they apply for the visa," he said. "This is the same principle that is applied to all other categories."
- Post Study Work Visa
- Talent (Accredited Employer) Work Visa
- Essential Skills Work Visa
- Religious Worker Work Visa
- Talent (Arts, Culture, Sports) Work Visa
- Long Term Skill Shortage List Work Visa
- Silver Fern Practical Experience Work Visa
- Trafficking Victim Work Visa
- Migrant Exploitation Protection Work Visa
- Skilled Migrant Category Job Search Work Visa
- Victims of Family Violence Work Visa
- South Island Contribution Work Visa
- Work Visa granted under Section 61 (provided the applicant held another eligible visa type within 6 months before being granted a Section 61 visa)
Some Critical Purpose Visitor Visas will be eligible as long as workers arrive in New Zealand and apply before 31 July 2022.
- Critical health workers for longer term roles (6 months or longer), and
- Other critical workers for long term roles (more than 6 months).
Applicants must meet the heath and character requirements, but overseas police certificates will not be required unless specifically requested by an immigration officer.
Other temporary visa holders are not eligible, such as visitors, students, working holiday makers, and seasonal workers like those on the Recognised Seasonal Employer Scheme or those who enter as short-term critical workers.