Liz Truss would seek to immediately reverse the rise in National Insurance contributions if she were to become prime minister, her campaign team says.
Ms Truss has already promised an emergency budget to stop the increase brought in by Rishi Sunak – her Tory leadership rival – when chancellor.
Her team thought the plan could not be implemented until April 2023, but now believe it would be within weeks.
But Mr Sunak said it would not benefit those who need help most.
He said: “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.”
He has said Ms Truss is “simply wrong” to rule out more cost-of-living payments, and has promised more direct help to those hardest hit by inflation.
Voting has started and the result is due to be announced on 5 September.
As well as her pledge to cut National Insurance contributions, Ms Truss – the foreign secretary – intends to cut taxes and suspend the green levy on energy bills.
Since April, workers have been paying more in National Insurance
– an extra 1.25p in the pound, although Mr Sunak later raised the threshold at which employees people start contributing.
Writing in the Sunday Telegraph, Ms Truss said she wanted to “immediately tackle the cost of living crisis”, adding: “I would hit the ground running by bringing in an emergency budget, charting a firm course to get our economy growing in order to help fund our public services and NHS.”
But Mr Sunak, who has argued that inflation must be brought under control before taxes are lowered, told the Sunday Times: “The priority for me is to not do things that make it worse.”
He said the public needed “clear-eyed realism and not starry-eyed boosterism”, and said his rival’s plans would give back less than £200 a year to many families, and “are not going to help very significantly” pensioners and those on low incomes.
Mr Sunak pledged to introduce a fresh multi-billion pound package of help.
It comes as former Labour Prime Minister Gordon Brown has said an emergency budget was needed now.
Writing in the Observer, he said Prime Minister Boris Johnson, Ms Truss and Mr Sunak should agree on one this week, warning “a financial timebomb will explode for families in October” when the energy price cap next rises.
A report commissioned by Mr Brown suggests some families are set to be £1,600 worse off per year.
The additional money from the government offered to low income households falls short of offsetting the losses they face, the research led by Prof Donald Hirsch at Loughborough University says.
The report says that the poorest families have suffered three major blows to their income from October 2021 to October 2022
That includes the loss of the £20 a week uplift to benefits, an annual rise in welfare payments that is below the current rate of inflation, and further increases in the energy price cap.
It found that the extra £1,200 of support offered by the government fails to bridge this gap because the flat-rate payments do not take into account households with larger families, and those with different needs.
“It is the urgent task of the next prime minister to ensure that families have enough to live, through this crisis and beyond,” Mr Brown said.
A government spokesperson said they understood people were struggling with rising prices and that was why it had made the extra £1,200 available to eight million of the most vulnerable households.
“Through our £37bn support package we are also saving the typical employee over £330 a year through a tax cut in July, allowing people on Universal Credit to keep £1,000 more of what they earn and cutting fuel duty by 5p, saving a typical family £100,” they added.