Mr Rowley said New Zealand probably had a similar situation to Australia, suggesting that about 14,800 of the estimated 148,000 liable male parents were wrongly paying child support.
A Family Court lawyer, Stuart Cummings, said he was aware of one mother who received payments from a man for some time then caught up with a former lover and realised that he was actually the father of her child.
She had the dilemma of deciding whether to tell the first man and risk losing the financial support she had been enjoying, said Mr Cummings, a family law spokesman for the Auckland District Law Society.
The revelations come after Australian authorities recently paid a Melbourne man nearly $12,000 when DNA tests proved he was not the father of his former partner's child.
Another Melbourne man is seeking a refund on six years of child support after discovering that another man fathered his 8-year-old girl.
Mr Scott said men could object to paying child support once the tax department had received a mother's application, and the Commissioner of Inland Revenue had the discretion to stop an order.
If a man disputes the decision he can appeal to the Family Court. Mr Cummings said the court could not order a DNA test but judges took a refusal into account when deciding a case.
He said that despite instances where men were paying child support for other men's progeny, women had an uncanny ability to know who the father was.
Many cases where men contested paternity resulted in their fatherhood being confirmed, said Mr Cummings.
Mr Rowley said some men knew a child was not theirs but were still happy to care for or pay child support.
He said it was often a tragedy when men contested paternity because, if unsuccessful, the father-child relationship could be damaged.