Employment Minister Michaelia Cash struggled to defend the Turnbull government’s claim that “low-paid employees are often found in high-income households” in a radio interview on Thursday.

Senator Cash, whose department is responsible for the government’s submission to the Fair Work Commission’s annual wage review, came unstuck when asked by 3AW’s Neil Mitchell to explain how many low- income workers had “fat rich parents at home”.

Referring to the submission, Mitchell asked the minister: “How many of these low-income earners, earning their $17 an hour, go home to wealthy support?”

Senator Cash responded that it “was not what the government is saying”.

“Yes it is,” Mitchell shot back.

As the radio presenter continually pressed the minister to explain the claim, Senator Cash batted it away by suggesting he was cherry-picking a line from the submission.

The submission noted “a significant proportion of the low-paid are members of higher-income households”.

“But what percentage of the 200,000 [minimum wage workers] are, as you say in your submission, found in high-income households?” Mitchell again asked.

“It’s not so much a percentage,” Senator Cash responded.

“Of course it is!” Mitchell said.

Senator Cash replied: “No, no, no, because you’ve got to actually look at the minimum wage review in total. You can’t just literally pick and choose a sentence.”

Throughout the 10-minute interview, an exasperated Mitchell repeatedly interrupted to bring Senator Cash back to the question.

Eventually he suggested: “Minister, you don’t have a figure here, do you?”

The Employment Minister said that it was “not that we don’t have a figure Neil”, which prompted Mitchell to respond: “You do have a figure? Give it to me!”

The Western Australian Senator strayed from the question again, before Mitchell again asked: “How many, what percentage?

“No, OK, I don’t have the figure, OK, but it’s not as simple as that, ” Senator Cash said.

“As I said, you pick and choose a particular line from the submission and then what you then lose is the totality of what the submission (is saying).”

Listen to the interview below

The government’s submission warned against “excessive increases” in the minimum wage, which it said would “reduce employment in award-reliant industries”.

It said 13.6 per cent of low-paid workers were in the “top two household income deciles”, while 17.9 per cent were in the bottom two tenths.

Mitchell told Senator Cash that the electorate would look at the line about low-paid workers and say: ‘You elite lot’. I mean, how many of the middle-aged women going and cleaning toilets in hotels today are going home to a rich sugar daddy?”

Senator Cash said Mitchell was “taking one sentence and distorting the fact”.

Labor seized on the interview on Thursday, with employment spokesman Brendan O’Connor telling reporters that “clearly Senator Cash didn’t know her own submission”.

Asked if he agreed with the claim in the submission, he told reporters: “I’m not going to accept on face value these assertions made by the government.”

Though he said it was true that there be low-wage workers in households where incomes “would be reasonably good”.