About 15 percent of visitors are still entering the country without the Electronic Travel Authority that became "obligatory" on 1 October.
Immigration NZ is being criticised for a lack of transparency over the rules, but said it had always planned to do a phased roll-out over the first few weeks.
The Electronic Travel Authority (ETA) means that people from 60 countries who previously didn't need a visa are now required to declare their passport details and any criminal history before they can travel to New Zealand.
After a multi-million dollar marketing campaign to ensure people knew about the system, Immigration NZ said there had been about an 85 percent compliance rate. But it was not aware of anyone being stopped and missing their flights because they didn't have the required ETA.
Immigration NZ Policy Director Nick Aldous said the phased roll-out had always been part of its planning.
"The obligation still sits on the traveller to obtain the ETA. How the system works is that the airlines won't be infringed for breaching their carrier obligations," he said.
"We've got some flexibility around the implementation and compliance in the first few weeks of implementation. We've also got our on-the-ground support staff in place. What we'll look to do next is ramp up the compliance activity and keep the on ground support in place, to support airlines and travellers ... and then finally, we'll pull our support staff and run the system."
Tourism Industry Aotearoa chief executive Chris Roberts said he supported the decision for a phased rollout - "because the biggest concern will be if this gets turned on and there's chaos."
But he said Immigration NZ should have been more transparent and encouraged visitors to get an ETA rather than telling them it was a requirement.
"I just think it would have been far easier to be upfront from day one and say look, we're taking it slowly, we encourage you to get one but the requirement to have one's being delayed for a few weeks, and we'll let you know whether there's a requirement," he said.
Nick Aldous said the key stakeholders were told about the phased approach that they were taking to compliance - it just wasn't advertised or marketed.
"It's important to get the message through that travellers are required to have an ETA and we are very concerned about making sure that that message doesn't get mixed and that guidance is clear."
The phased rollout is due to go until the end of October, after which visitors without an ETA can expect to be stopped before boarding flights to New Zealand.