The Government says it will look at a "quirk" in immigration policy that means some workers have to leave the country and fly back in to be eligible for next year's one-off residence visa.
Some overseas medical staff in hospitals and aged-care facilities are among those whose visa type exclude them being one of next year's 165,000 new residents.
People already working in New Zealand had to fulfil the criteria the day before the policy was announced, at the end of September.
But they would qualify if they arrived in the country on critical worker visas between now and July, prompting some to consider the unusual option of leaving New Zealand in order to become residents.
One 28-year-old hospital doctor told RNZ last month she had worked as an emergency department doctor but went onto a working holiday visa so she could easily do locum work.
Not being on one of the work visas the Government named in the residence policy had left her weighing up flying out and returning on a critical healthcare visa in order to settle permanently - an option she said was annoying and made no sense.
"The criteria are broad as they are so we're happy to look at the situation in particular around those health workers," said immigration minister Kris Faafoi. "There's been a longstanding border exception for them, they're the kind of people we would like to stay in the country long term as well.
"I don't know the particular situation that they're in but we can always look at that situation. I think if they have ticked one of the three boxes - in terms of being settled, skilled or scarce - they can be eligible for the visa. If a quirk of their situation means they may have to come in and come out we'll have a look at it, but the criteria are pretty broad when 165,000 people are eligible for it."
Other migrants found themselves ineligible because their visas were based on their partnership with another visa holder, but no changes are expected to that policy nor to the exclusion on PhDs and other students who had been working in critical areas.
The new one-off residence visas open next month and the first eligible applicants are starting to prepare.
Immigration New Zealand (INZ) has published its internal instructions which bring the policy into operation.
Among the details is an exemption from providing an overseas police check.
Potential residents usually have to show any criminal history in countries where they have lived for more than a year in the past decade.
That will now not be necessary unless it is requested by an immigration officer. INZ will still request New Zealand police checks.
Anyone who has provided a medical certificate in the past three years will not have to undergo another assessment if they had an acceptable standard of health, and all others can provide a Limited Medical Certificate.
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