New Zealand First claims Whanau Ora funding is being used to help "overstayers" remain in New Zealand.
NZ First leader Winston Peters claimed in Parliament an immigrant with a history of family violence, child neglect and drug abuse received help from Whanau Ora in an attempt to get his residency application approved.
Whanau Ora Minister Tariana Turia acknowledged the Whanau Ora programme was "assisting that person with all the issues that are confronting him, including the family violence issues".
"The issue of whether he gets to stay in New Zealand will depend on the outcomes of that."
But she rejected suggestions it was a rort and said the person concerned was just one of 18 family members being dealt with by the Whanau ora provider.
The scheme, a flagship policy of the Maori Party, has been under fire recently over a criminal case in Dunedin which revealed Whanau Ora funding was obtained by a gang for drug money.
In a statement, Mr Peters said New Zealand taxpayers were being expected to foot the bill for imported problems.
"The Whanau Ora scheme is a tangled mess but it hasn't stopped us from finding illegal 'overstayers' with serious substance abuse issues who are being given taxpayers money."