The level of arrivals has levelled off in recent months. However, arrivals only account for half of the strong pick-up in net migration since 2012, Westpac said.
"New Zealanders are being encouraged to stay onshore or come back from overseas by our positive economic conditions," the bank said in a commentary.
While net migration is continuing to run at record annual highs, there are signs of short-term visitor arrivals flattening off.
"Net migration flows will continue to support overall economic growth, even though the flow is likely to soften over time," ASB said in a commentary.
"Visitor arrivals growth is, however, easing, implying tourism earnings growth will also soften," the bank said.
Looking at the composition of arrivals, those coming from the United Kingdom are showing little sign of changing their mind, the bank said.
"This could be a Brexit-effect, with around 12 per cent of NZ arrivals citing the UK as their last residence," it said.
South Africa is also trending higher, now up to around 4 per cent of arrivals, with a combination of push and pull factors increasingly making NZ a popular choice for South Africans.
For the first time since August 2014, annual short-term visitor arrivals did not mark a new record high.
"However, before alarm bells start ringing, the dip was only around 600 visitors over 12 months and could be down to the timing of Easter in 2016, which was in March," ASB said.
ANZ said it expected visitor arrivals should also remain strong, boosted by the World Masters Games, which are under way in Auckland.
The British and Irish Lions rugby tour in June also looms large as likely to boost overall visitor numbers.
"While these types of events have the potential to displace other visitors, or see those that were going to come anyway simply shift the timing of their travels to coincide with these events, we are still expecting to see some decent arrivals figures over the next few months," ANZ said.
As this year's general election looms, migration is shaping up as a key issue.
Last week the government announced it is committed to a "Kiwis first" immigration policy, making it harder for firms to hire overseas with new restrictions on temporary work visas for anyone earning less than the median wage.
Labour leader Andrew Little has targeted immigration as a key election year issue, calling for numbers to be cut by the "tens of thousands".
Today's figures underlined the need for an "urgent rethink" on current arrival numbers," Little said.
"We need to pause and rethink our current settings. We need to ensure the people arriving have the skills we need and that our cities can cope with any increase in numbers."