"Inevitably people who rely on concocting false backgrounds and relationships will be found out," he said. "It's just a matter of when.
"Identity fraud is a major challenge for us - the integrity of our immigration system is paramount, given its importance to New Zealand and our international reputation as a safe and secure country."
Mr Elms said INZ is continuing to strengthen its work with international partners, including through the development of a biometric programme, to enable greater detection of people attempting identity fraud.
The sentences, handed down in the Auckland District Court, were:
Shinder Kaur, 54, and her husband Jagroop Singh also known as Ram Singh (two charges each under the Immigration Act 1987): 4 months' home detention
Manpreet Singh, 27, (male): 8 months' home detention (two charges)
Paramjit Kaur, 38 (female): 10 months' home detention (three Immigration Act and one Crimes Act charges).
They had admitted all charges. All are from Manurewa.