Immigration staff are working through the Christmas and New Year break to try to clear a backlog of visas for asylum seekers.
Its head of operations at Porirua has apologised to those affected, who have struggled with new requirements to provide and pay for medical and police checks.
In at least one case, delays left an asylum seeker unable to work and buy food and medication after his work and interim visas both expired.
He slept in his car because he could not pay the rent.
He was told by an immigration official he was not unlawfully in the country.
After RNZ contacted Immigration New Zealand, he was issued another work visa.
The Cameroonian man, who said he escaped jail there after being jailed as an activist, had a full-time job at an online travel agency in Auckland when his interim visa ran out.
"I was even thinking that it [would be] better for me to be in jail because I could eat," he said. "I can't even eat, I can't even pay my rent. That was why I was asking the [case] officer, 'how do you expect me to survive?'
"I was thinking maybe I should just go to jail and tell them that I need a place to stay because I don't know where to stay, I've been living in my car."
Immigration lawyers and advocates had lobbied the government about the risks to asylum seekers and their families having to ask authorities in their home countries for police checks.
They also said many would not be able to afford medical checks. Refugees cannot be rejected because of poor health.
In an email last week the head of operations at INZ Porirua, Craig Pontifex, said it would refund those who paid for medicals since the new system was introduced in October.
A requirement for chest x-ray screening for tuberculosis would remain but those checks would be government-funded.
He said immigration officers could waive character requirements (police checks) if such checks were not available or unduly difficult to obtain.
"It should also be noted, if a police certificate cannot be provided or may place the applicant, their family or any other person in any harm from their country of citizenship, a statutory declaration will be accepted," he said.
INZ would also help cover those costs, he added.
A queue of temporary visa applications for people waiting for their asylum cases to be decided had built up.
"INZ is setting up a dedicated team of immigration officials whose sole task will be to assess and decide these applications," he said.
"In the meantime we will continue to assess and decide those applications as and when the medical and character requirements are met. INZ Porirua will not be closing over the Christmas and New Year period.
"New Zealand has a long and proud history of refugee resettlement. New Zealand is committed to fulfilling its international humanitarian commitments to provide protection to refugees who are not able to return safely to their home country.
"We sincerely apologise for any issues and hardship that the implementation of these processes will have caused over the recent months."
The case is the latest in a series of delays to residence and temporary visas.
It follows the cases last month of more than 100 immigrants who were told to overstay while their applications were processed https://www.rnz.co.nz/national/programmes/checkpoint/audio/2018724739/immigration-nz-allows-overstayers-as-it-catches-up-on-paperwork
In a statement, INZ's Border and Visa Operations general manager, Nicola Hogg, said all those people had since been granted a matching temporary visa while their application was being assessed.
"We also amended our process so that people who have submitted a temporary partnership application and who are approaching the end of their interim visa will be granted a further matching visa while that visa application is assessed," she said.