Suspicious visitors to New Zealand with too many credit cards or with plans to see boomerangs and kangaroos are among the rising number of people being refused entry to the country.

While some who weren't allowed in over the past few years were turned away for slightly comical reasons, others trying to get in had a more criminal flavour to their plans.

In the 2015/16 year, an apparent tour group of Taiwanese people was referred to Immigration NZ after Customs found a number of dodgy items in their luggage, including mobile devices, IT cables, remote controls, SIM card adaptors, and bolt cutters.

All 19 of the group, including the alleged tour guide, refused to be interviewed and would not provide any information to Immigration about the reason for their travel. They instead requested to be sent home and were on a plane back to Taiwan within 13 hours of arriving in New Zealand.

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Further information gathered about the group indicated they were hoping to set up an outbound call centre in the country, selling bogus investments over the phone.

The group was a small fraction of the 1371 people refused entry in that year, a figure which has been steadily rising since 2011/12.

In that year, 790 people were denied entry. From then until 2015/16, a total of 5309 people didn't make the cut.

Figures released by the Ministry of Business, Innovation and Employment show the number of people being booted out for having a non-genuine reason for travelling to Aotearoa is also rising - from 396 in 2011/12, to 708 five years on.

"The vast majority of travellers are seeking to enter New Zealand temporarily - typically for a visit, to work, or to study," MBIE compliance, risk and intelligent services general manager Nicola Hogg said.

"Immigration officers assess whether a person is bona fide. This means we must be satisfied that a person is genuine about their reasons for coming to New Zealand and about what they will do while they are here."

Immigration was distrustful of one traveller picked up on by the Australian Border Force.

The Russian passenger was in transit in Brisbane when authorities found him to be in possession of 64 credit cards, 100 SIM cards, two passports, and six mobile phones.

He couldn't provide rational explanations for having the items when he was interviewed in Christchurch, and was not thought to be a genuine visitor.

Other entry denials in the last couple of years included a Mexican man who "needed a break" from his home country due to "security concerns" around the legalisation of cannabis.

According to an annual report by Immigration, the man initially tried to get into New Zealand claiming he wanted to see beaches and gardens, kiwis, kangaroos, and boomerangs. He had no accommodation booked and was planning to rent a house in Christchurch.

Another traveller was turned away because she had no outward ticket - it had been cancelled and refunded - and she had little knowledge of New Zealand.

"She claimed that she wanted to see the Lord of the Rings locations and knew that Harry Potter was the main character in the film," the report said.

Aside from being a non-genuine visitor, other top reasons for people to be refused entry included "red zone referral", concern over character, and being a passenger in transit.

A red zone referral was one in which the person is referred to Immigration by Customs after questionable items are found in their luggage.

Being a passenger in transit refers to a traveller who arrives in New Zealand while on their way to another country.

Some mistakenly head to arrivals when they leave their plane and are then processed as an arriving passenger where they are then denied entry. Other times, the passenger seeks the opportunity to sightsee in between their flights and are refused permission.