Immigration Minister Michael Wood has admitted "pain points" in the visa processing system as more than 35,000 visitors wait for visas.
Almost half of all people asking for visas to visit New Zealand since July have not yet been told whether they can come.
"Upfront I want to acknowledge there have been some pain points in the system as processing has commenced after those significant border closures," Wood said.
"But in the context of nearly 100,000 applications received since the 31st of July, we're now seeing real progress back towards a steady state."
Wood also said he would keep an open mind on whether to help overstayers and international students whose post-study work visas expired while they were overseas during the pandemic.
Immigration New Zealand figures show fewer than half of the 14,000 accredited employer work visas approved since the start of July have been processed.
"We are now seeing the rebalance having an impact, we're about three or four months into the new settings that kicked in from July 4. The accredited employer work visa provides a streamlined, uncapped employer-led process that helps us fill skill shortages and compete internationally for top talent."
More than 31,000 working holiday visa applications have been approved since March, he said, and caps in that scheme had been doubled, allowing thousands more working holidaymakers to come in.
But while work visas have also got off to a slow start, green-list residence visas seem to be moving faster.
Of more than 400 Straight to Residence applications that have come in during the past six weeks since it opened in September, 61 have already been approved.
Wood last week said the border reopening had been a unique situation to deal with, but promised more transparency in the immigration system and said New Zealand's "sugar hit" of cheap migrant workers was over.
"Businesses have told me that they need certainty, a steady supply of highly-skilled labour and the ability to put forward a competitive offer during times of massive global labour shortages.
"Migrant communities have spoken to me about fairness, protection from exploitation and opportunities to put down roots and invest in a future in New Zealand. It's also clear that people want clarity on our immigration rebalance, the rationale and also the pathway."
He was questioned about what action he might take on post-study work visa holders, one of the few groups of migrants already resident in New Zealand were not given border exemptions during the pandemic.
An estimated 5000 migrants were described as being stranded or 'stuck' overseas when the border closed.
"I gave a good-faith commitment to look into it and that is what we are doing," he said, during his skilled migrant and parent category announcements in Mount Roskill, Auckland, on 12 October.
"I am willing to look at some of our settings there, I haven't concluded that process yet but I have received advice on it and I am working through that issue.
"But I do want to be really clear on one point: I disagree in respect of people oversees who are able to offer work and skills in New Zealand - I disagree with the characterisation of 'stuck'. Every single one of those people, where there's a need in New Zealand, has a pathway through the accredited employer work visa.
"The employer just needs to go through the simple process and needs to be willing to pay the median wage and they are able to then recruit offshore - whether it's a chef or anyone else - where there is a shortage within New Zealand."
'The only way to be fair'
Advocates are also pushing Wood to regularise the visa status of an estimated 30,000 overstayers, and he said that would need to be carefully weighed up.
"Our immigration system by definition needs to be based on fair and consistent rules that we apply, that in some ways is the only way to be fair. Regularisation by definition says if you have broken the rules and gone outside of that, you will get a free pass.
"And one of the more difficult things if we go down that path is what do I then say to the person who the day before I made that decision played by the rules and left New Zealand voluntarily who misses out.
"There are arguments on both sides. And that is why with such a big and complex issue we will not be rushed into making a decision.
"I have given commitments for us to be open-minded, to consider this issue and others when we get through the current work programme, but we will have to weigh up those different imperatives and take good advice on board before we make a decision."