Welfare experts have ridiculed a government claim that thousands of parents on government benefits earn more than if they had a job, saying it is built around a mathematical mistake.

The claim, published in The Australian on Friday and backed up by Social Services Minister Christian Porter, is that single parents with four children can get payments totalling $52,523 per year if they don't work but only $49,831 after tax if they work and receive the median full-time wage.

Mr Porter said the data showed taxpayer-funded benefits could be providing a ­disincentive to work, a systemic flaw that required government ­attention. "What is not in any recipients' best interest is to be deprived of the incentives to reduce income from welfare with income from work," he said.

Treasurer Scott Morrison backed him saying it was "a crying shame that some Australians would have to take a pay cut to get a job in this country because of the way our welfare system works".