Liz Truss and Rishi Sunak are coming under growing pressure to explain how they would help British families with the cost of living crisis this autumn.
With inflation set to spike above 13% in October, the energy price cap expected to surge and a recession forecast by the year's end, economic policy has become the defining issue of the Conservative leadership campaign.
A row broke out over the weekend after Ms Truss told the Financial Times that she planned to lower taxes rather than offer handouts.
This prompted a swift rebuke from Mr Sunak, who said it is "simply wrong to rule out further direct support" for struggling families this winter.
Supporters of Ms Truss later told Sky News that her remarks had been "misinterpreted".
Penny 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."
In other developments, former Labour prime minister Gordon Brown has made his second intervention in as many days.
Mr Brown, himself an ex-chancellor, is calling for the COBRA emergency committee to sit in "permanent session" during the current crisis.
He is also calling for parliament to be recalled as a matter of urgency unless Boris Johnson and both Tory leadership candidates can agree on an emergency budget in the days to come.
Writing in the Daily Mirror, Mr Brown said: "Even if Boris Johnson has now gone on holiday, his deputies should be negotiating hard to buy new oil and gas supplies from other countries and they should be urgently creating the extra storage capacity that we currently lack."
And he warned that some of the tax cuts proposed throughout the leadership race "will not benefit those who are really poor".
Over the weekend, a report commissioned by Mr Brown warned some low-income families are up to £1,600 a year worse off as a result of the cost of living crisis following a triple blow to their earnings - even after government support is taken into account.
While working-age households on Universal Credit and other means-tested benefits are getting up to £1,200 of additional help, poverty expert Professor Donald Hirsch said these measures have been overshadowed.
Tory MP Damian Hinds, one of Mr Sunak's supporters, has conceded the existing package was not enough in these "extraordinarily difficult times".
He told Sky News: "Things have been getting worse even since that was put into place in terms of projections for energy bills... and [Mr Sunak's] been clear that more may well be needed and he is ready to do that as required."
Newly released research by the Labour Party suggests £1 in every £5 spent by pensioners this winter will go on energy bills - and "fantasy tax cuts" proposed by Tory leadership hopefuls won't benefit older people.