Truss who is the favourite to clinch the position according to pollsters, said she would act immediately to help with bills.
But she offered no details, saying she would need time in office first in order to finalize exact proposals.
Her rival,Rishi Sunak said he would target further payments at the poorest.
One of the two contenders will be announced as the next Tory leader today and will replace Boris Johnson in Downing Street tomorrow.
They have come under pressure to spell out how they would protect households with rising bills, as well as give help to businesses, which are not covered by the domestic price cap.
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