Liz Truss has pledged to "immediately" reverse the increase in National Insurance if she wins the race for Number 10.
The foreign secretary said she would make the move in an emergency budget in September while announcing other tax cuts.
But leadership rival Rishi Sunak hit out at her plans, contrasting his "clear-eyed realism" with the "starry-eyed boosterism" of Ms Truss.
Arguing for inflation to be brought under control before taxes are cut, Mr Sunak accused the foreign secretary of taking a "gamble" with savings and pensions.
On Saturday, Ms Truss rejected "handouts" to help households through the worst income squeeze in 60 years - although her team insists this does not mean no more direct support.
Former leadership hopeful Penny Mordaunt said on Sky News this morning that Ms Truss' comments about handouts had been "misinterpreted".
She said 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 that back in ever more complicated ways."
Ms Truss argues her tax plans 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."
Meanwhile, Mr Sunak has pledged billions more to help families through the cost of living crisis, according to the Sunday Times.
He told the newspaper that if he became prime minister he would "go further" than the support he announced when he was chancellor, once there was "certainty about exactly what bills are going to be in the autumn".
However, it is not clear how much further Mr Sunak would be willing to go.
When asked on Sky News if the former chancellor would expand the energy support scheme, his supporter Damian Hinds MP said: "I am not in a position to set out exactly what he will do."
However, he added: "His track record is absolutely taking the required action, doing it in a timely, time limited, targeted way."
Tax cuts could fuel inflation - predicted to top 13%
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.
Earlier this week, in an interview with the Financial Times, Ms Truss insisted she would press ahead with tax cuts, despite claims they would fuel inflation - already forecast to top 13%.
Former deputy governor of the Bank of England Charles Bean told Sky News Ms Truss's plans "are not particularly well targeted in terms of dealing with people who are most hit" by the energy price spike.
He added: "The existing package that previous chancellor Rishi Sunak put in place had more conscious targeting towards poorer households and I think it's pretty clear that any fiscal manoeuvre we have at the moment should be primarily directed towards them rather than more broadly."
Tory voters swing behind Truss
Despite the warning, Ms Truss has taken a seven-point lead as best prime minister against Mr Sunak (27% to 20%) and a 26-point lead among 2019 Conservative voters (48% to 22%).
Research from Opinium found on all leadership attributes, 2019 Tories are more positive about Ms Truss than two weeks ago and more negative about Mr Sunak.
A third of all voters (34%) think the government should keep taxes and spending on public services about where they are now, while 26% think there should be an increase in both.