Immigration New Zealand says if a group of banned rappers want to come to New Zealand as a group in the future, the application would be assessed on its merits at the time.
Odd Future, known for sexually violent lyrics, is banned from entering New Zealand. The group was scheduled to perform at the Rapture 2014 concert in Auckland on Saturday night.
Border operations manager Karen Urwin said the issue is with Odd Future as a group and if they wanted to come as individuals there would be no problem.
She said the Immigration Act is clear that New Zealand can refuse to let people in who pose a risk to public order.
An organisation which called for Odd Future to be banned is being flooded with abuse.
The Stop Demand Foundation said it was being targetted by angry fans even though it had nothing to do with Immigration New Zealand's decision.
Spokesperson Denise Ritchie said vitriol and abuse was being left on her phone, the foundation's facebook page and on email, and it's at the point where she is having to have someone else monitor what's coming in.
Ritchie said Immigration New Zealand made the decision her group wanted.
She told Radio New Zealand's Morning Report the band's lyrics are hate speech which desensitise people to rape.
However, music writer Duncan Greive told the programme the move to ban the group may provoke a reaction from fans, and from Eminem, the headline act at the concert.
Variety magazine music critic Andrew Barker said Odd Future has been the flashpoint for debate among music critics and moral watch-dogs since it emerged, so the furore in New Zealand is no surprise.
Although the band has attracted attention for fan violence, as well as damaging equipment on-stage, he said none of its antics have gone beyond those of other notable groups.
He said the accusations of inciting violence against police sound much more serious than the evidence suggests.
Odd Future's manager Christian Clancy tweeted, "sorry new zealand apparently this group of kids that have inspired the shit out of me for the last few years are a threat to society. ... and thanks for the hour before flight heads up. after approving and issuing visas."