While the voyage to New Zealand from places such as Indonesia and Sri Lanka is potentially far more perilous than trying to reach Australia, Key said people-smugglers and asylum-seekers were willing to take the risk in the wake of Canberra's clampdown.
"We take this very seriously ... we know it's very hard to come to New Zealand, no one's arguing it's an easy distance or journey," he told TV3.
"But the reality is that as Australia closes down as a destination for asylum-seekers, they are trying to open up new frontiers and one of those is New Zealand."
Australia was facing record numbers of asylum-seekers before conservative Prime Minister Tony Abbott was elected last year on a populist platform of "turning back the boats".
Under Canberra's policy, any asylum-seeker arriving by boat is transferred to remote centres in the Pacific for processing and permanent resettlement.
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No refugee boat has yet reached New Zealand but Sri Lankan police in February arrested 75 would-be asylum-seekers