Would-be Tory leader David Davis has pledged to tear up the party's "timid" tax policies - promising a cut of £1,200 a year for the average family.
Mr Davis says the plan does not involve public spending cuts
Putting the issue at the heart of his campaign, Mr Davis wants £38bn a year tax cuts by the election after next.
The cash would come from slower growth in public spending and not cuts in services, he said.
It comes after leadership rival David Cameron said the party could not win elections with tax cuts alone.
In an apparent swipe at Mr Davis, Mr Cameron said: "The Conservative Party will never convince people that we can be trusted to run the economy if all we talk about is cutting taxes and cutting spending.
"That's not an economic policy, that's a tax policy. Tax is a vital part of economic policy - but it is only a part."
POSSIBLE TAX CUTS
8p cut in the basic rate of income tax, from the current 22p to 14p
OR cut income tax by 2p, reduce the main rate of corporation tax by 3p and scrap inheritance tax, stamp duty and capital gains tax entirely
Mr Cameron has not outlined specific tax cuts, saying the details of the Tory manifesto for the next election should not be written now.
On Friday, Mr Davis hit back at his rival, saying he "could not disagree more" with those saying tax policy should not be made now.
His tax cuts would be made possible by a big reduction in the growth of public expenditure, which he wants to increase at a slower rate than that of the economy.
He admitted it would take some time to persuade the public that reducing tax rates would eventually increase tax revenues by boosting economic growth.
But he argued "we cannot afford to be frozen in the headlights of the Blair settlement" of increasing tax and spending.
"The Tory party in the last decade has been too timid on tax," he said.
The shadow home secretary insisted the plan was in line with moderate One Nation Conservatism and would help the poorest in society the most.
He is not giving details of exactly which taxes he would cut.
But he says the plans could lead to an 8p reduction in the basic rate of income tax, from the current 22p to 14p, representing a saving for the average family of about £1,200 a year by 2014/15.
Alternatively, they could be used to cut income tax by 2p, reduce the main rate of corporation tax by 3p and scrap inheritance tax, stamp duty and capital gains tax entirely.
There could also be transferable tax allowances for families with children.
And the proposed savings were only a "first step" as cutting taxes would help the economy grow, he said.
BBC economics editor Evan Davis said the plans were similar to those promised by the Tories before the election - although under David Davis they would be enacted more quickly.
He said the savings could "feel like a cut" because Mr Davis was promising to raise spending faster than inflation, but inflation in the public sector rose faster than inflation generally.
Mr Cameron says the proceeds of economic growth should be shared between tax cuts and public services, but competitive tax rates are needed for a dynamic economy.
His spokesman said: "It is encouraging to see that David Davis has now confirmed he supports that approach and that there is a lot of common ground between them on this issue."
Mr Cameron is meeting Tory activists in Bexhill, East Sussex on Friday.
Ballot papers for the 300,000 Tory members who will decide the contest will be sent out next week. The new Tory leader will be known in December.