With some international flights allowed into Auckland, regional flights are halted until at least Tuesday evening, while trains have been cancelled and the Harbour Bridge remains under constant review.
Flights in and out of Auckland, Hamilton, Tauranga and Taupō are all cancelled until at least midday on Tuesday.
Air New Zealand said it made the decision to keep customers, staff and aircraft safe.
International flights in and out of Auckland have also been interrupted.
Air New Zealand chief executive Greg Foran told Morning Report with winds in the city easing, four international Air New Zealand flights were scheduled to land in Auckland Monday morning, with two having already arrived. Another one had been due to arrive from Australia, but would be diverted to Christchurch if there were safety concerns, he added.
"You can only fit so many planes down in Christchurch and can only get so many hotel rooms at short notice," Foran said.
"So, what you're trying to do here is sort of thread the needle and come up with a solution that gets you in the best position fundamentally to recover as quickly as you can when you can get open."
He said the wind had been 20 knots, blowing from the east of Auckland airport this morning, but the company was expecting that to change and get worse.
"You can only fit so many planes down in Christchurch and can only get so many hotel rooms at short notice" - Air New Zealand chief executive Greg Foran
"We don't have the same benefit that some others do you know, where if you're on the Harbour Bridge, you can sort of change the electronic scoreboard and suddenly you're open," he said.
"We take a little bit longer to get up and running. And at this stage, that will be our position until midday on Tuesday). But we are meeting regularly and we assess the situation. But at this stage, you know if we get going and it'll probably be a day tomorrow.
The company has also brought a flight out of New York, making the decision yesterday.
"It's a 17-hour flight back and the pilots made a good decision on the way down - they've said based on what they were hearing about the weather in Auckland, they've actually decided to stop and Rarotonga," Foran said.
"So they did that a few hours ago, so that planes actually sitting in Rarotonga, and then we'll work out how we're going to get it back from Rarotonga back into Auckland."
The company was paying for accommodation for those affected, although Foran said normally, in the case of a weather event where there had been plenty a notice of what was gone, no refunds were given, but full flexibility was offered.
Domestic travellers should be able to fly on scheduled routes on Wednesday across North Island airports.
"They'll generally be fine, providing we're operating the network," Foran said.
"What we need to do now is to quickly work to recover the thousands of people that have been disrupted from today and half of tomorrow. So they're the ones that we end up having to shuffle around and try and get on flights.
The company's call centre was inundated this morning, with a waiting time of three-four hours at 6am this morning. Foran said there was 500 staff working at the centres and he expected the waiting time to be reduced.
"If tracks remain closed, we will have rail placements" - Auckland Transport executive general manager of safety, Stacey van der Putten
Meanwhile, Auckland transport is urging residents to stay home until Tuesday unless it is absolutely urgent.
Auckland's Harbour Bridge has been partially closed, but Waka Kotahi has warned it may close periodically as winds increase.
Trains have been suspended until at least 3pm today, with most replacement buses not immediately available. Normal buses are still running but with delays, detours, and cancellations.
Auckland Transport executive general manager of safety, Stacey van der Putten, told Morning Report that situation was constantly changing and the body was following weather advice and ensuring clear lines of communication to Aucklanders on the travel options open to them.
She said she was waiting on an update from KiwiRail on the state of the train network.
"We don't have a full rail replacement option at the moment. We are working with our operators to understand what we can do on the provision that we get an update from here we were out this afternoon," she said.
"We don't have a full rail replacement option at the moment.
"We are working with our operators to understand what we can do on the provision that we get an update from KiwiRail this afternoon.
"So, if tracks remain closed, we will have rail placements. The team are doing the best to get them up and running so that can slot them when necessary."
She said key routes where there was essential service coverage, like routes to hospitals, would be prioritised.
The road network was functional, but a question mark remained over Auckland's Harbour Bridge, which was currently opened, with speed restrictions and less lanes available, she said.
The bridge, which was close yesterday due to safety concerns, may close again, depending on the changing weather situation.