UK Deputy Prime Minister Dominic Raab took aim at the foreign secretary's emergency budget plans in one of the most strongly worded interventions of the leadership race so far.
With Ms Truss on the back foot over the cost-of-living crisis, Mr Sunak promised, if elected prime minister, to unveil more support for households once the size of autumn energy bills becomes clear.
The two candidates will set out their pitches at the latest round of hustings on Tuesday in Darlington, a constituency in the north of England which switched from Labour to the Conservatives at the last election.
A Truss backer, Defence Secretary Ben Wallace, criticised the Tory infighting on a campaign stop in Yorkshire by saying that "blue-on-blue is not going to help the Conservative Party win the next election".
Ms Truss used the visit to an aerospace company in Huddersfield to promise a tough line on defence, repeating a promise to increase military spending to 3 per cent of GDP.
But polls show the economy is voters' top concern two years from the next general election, as fuel prices drive the highest inflation in decades and economists predict a recession to add to Britain's woes.
Analysts Cornwall Insight said on Tuesday that the price cap is expected to soar to around £3,582 ($,4,340) per year in October, from £1,971 ($2,388) today, before rising even further to about £4,200 ($5,088) in the New Year.
Ms Truss, who leads Mr Sunak in polls of the Tory race, came under pressure after telling the Financial Times that she would tackle the problem "in a Conservative way of lowering the tax burden, not giving out handouts".
She and her allies have since sought to clarify that further government support was not being ruled out. Ms Truss said on Tuesday that she does not believe in “taxing people to the highest level in 70 years” and then “giving them their own money back”, in a thinly-veiled swipe at Mr Sunak's record as chancellor.
But Mr Raab wrote in The Times that focusing on tax cuts "isn't Conservative politics … it's bad politics".
"If we go to the country in September with an emergency budget that fails to measure up to the task in hand, voters will not forgive us as they see their living standards eroded," he said.
"Such a failure will read unmistakably to the public like an electoral suicide note and, as sure as night follows day, see our great party cast into the impotent oblivion of opposition."
Mr Raab's turn of phrase is most commonly associated with the 1983 Labour Party manifesto, a hard-left document described at the time as the "longest suicide note in history".
Penny Mordaunt, a former leadership candidate who now backs Ms Truss, defended the foreign secretary by saying Ms Truss "wants to do more" and that extra support was not being ruled out.
Conservatives on the campaign trail - in pictures
But Mark Harper, another Sunak backer on the Conservative benches, told Sky News that cutting taxes would not do much for poorer people who pay little money to the Treasury anyway.
"There’s a very big difference between large, permanent, unfunded tax cuts that go to the wealthiest in society, rather than targeted help," he said.
Mr Sunak said he would aim to keep any one-off borrowing to an “absolute minimum” by seeking efficiency savings across government departments.
He said he would announce details of new support once energy regulator Ofgem reveals the autumn price cap at the end of this month.
Ofgem said last week that the price cap would now be raised every three months, rather than every six, because it is "not in anyone’s interests for more suppliers to fail and exit the market".