Liz Truss was not ruling out future cost of living support when she said she would reject "handouts", her supporters have said, with prominent backer Penny Mordaunt claiming the comments were "misinterpreted".
Leadership rival Rishi Sunak attacked the comments saying the foreign secretary needs to "get real", while claiming her plan to cut taxes immediately will do little to help the most vulnerable.
But Penny Mordaunt, who is backing Ms Truss to become the next prime minister after her own leadership bid failed, claimed on Sky News that her remarks had been "misinterpreted".
Ms Truss told the Financial Times that as prime minister she would "look at what more can be done" to help families facing spiralling fuel bills.
But she added: "The way I would do things is in a Conservative way of lowering the tax burden, not giving out handouts."
Ms Mordaunt insisted Ms Truss was making a "general point about the merits of enabling people to keep more of what they earn".
"She's not ruled out all future help. In fact, part of her the reason for her putting an emergency budget forward is to really address some of these issues," Ms Mordaunt said.
"What she has, I think, rightly challenged is the wisdom of taking large sums of money out of people's pockets in tax and then giving some of that back in ever more complicated ways."
It comes days after Ms Truss claimed the media had "misrepresented" her proposal to link public sector pay to local living costs as she U-turned on the controversial policy.
Backers of Mr Sunak have seized on Ms Mordaunt's comments, with Tory MP Mark Harper tweeting: "Stop blaming journalists (again) - reporting what you actually say isn't 'misinterpreted'.
"This kind of thing happened under the current PM & hugely damaged trust in us all. So just what does 'not giving out handouts' mean then? Seems pretty clear…"
Simon Hoare, the Conservative MP for North Dorset, said: "So, 2 'misinterpretations' in a few days!! The country needs a serious PM who doesn't make it up as it goes along."
However, a source from the Truss campaign told Sky News: "We didn't rule out further support, if you look at what Liz actually said. The point she's making is a broad one of principle, not literally ruling out any more support."
Ms Truss has pledged to "immediately" cut taxes if she wins the race for Number 10, adding that she would call for an emergency budget and tackle the cost of living crisis by "reversing the rise on National Insurance".
She is pressing ahead with the plans despite claims they would fuel inflation - already forecast to top 13%.
Ms Truss argues her £30bn plan for tax cuts will make the economy more competitive and could prevent a looming financial crisis.
In an attack on Mr Sunak's plans, she told reporters during a campaign visit to the West Midlands on Saturday: "Having the highest taxes for 70 years is not going to deliver that economic growth, and it's leading our country to a recession."
But Mr Sunak hit back, contrasting his "clear-eyed realism" with the "starry-eyed boosterism" of Ms Truss.
The former chancellor is arguing for inflation to be brought under control before taxes are cut, accusing the foreign secretary of taking a "gamble" with savings and pensions.
He has pledged billions more to help families through the cost of living crisis when bills are expected to rise again this October, according to the Sunday Times.
He said: "We need to get real about this situation.
"It's simply wrong to rule out further direct support at this time as Liz Truss has done and, what's more, her tax proposals are not going to help very significantly people like pensioners or those on low incomes, who are exactly the kind of families that are going to need help."
The row comes after a report found some families are up to £1,600 a year worse off because of the cost of living crisis - even after government help is taken into account.
Former prime minister Gordon Brown, who commissioned the report, is urging Boris Johnson, Rishi Sunak and Liz Truss to agree an emergency budget this week - and says time is running out to update the Universal Credit payments system before the next energy price cap hike.