Rishi Sunak says it would be "wrong" to rule out more payments to help families with the cost of living.
It comes after leadership rival Liz Truss said she'd deal with the crisis with tax cuts, not "handouts."
Ms Truss said she would go ahead with vast tax cuts if she becomes prime minister, despite concerns they would further drive up rising prices.
Asked how she would help families with spiralling bills this winter, the Tory leadership hopeful told the Financial Times: "Of course, I will look at what more can be done.
"But the way I would do things is in a Conservative way of lowering the tax burden, not giving out handouts."
It comes after Mr Sunak was slammed over a leaked video showing him admitting to having diverted funding from "deprived urban areas" towards more prosperous towns has divided Tory figures, with Labour labelling it as "scandalous".
Energy consultancy Auxilione this week said the Government's price cap, which sets bills for more than 20 million households in Britain, could reach nearly £4,000 a year from January.
New analysis from the Office for National Statistics (ONS) also shows that close to half (44%) of UK adults who pay energy bills found it very or somewhat difficult to afford them in the last two weeks of July.
In a statement, Mr Sunak said: “We need to get real about this situation.
"It’s simply wrong to rule out further direct support at this time as Liz Truss has done and what’s more 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.”
But he said any additional help he would introduce as Prime Minister would depend on "the situation."
He said: "Yes I will look at doing more and particularly for families like pensioners for example where I said that this winter they can get an extra payment worth up to £300.
"There are things like that we will have to look at depending on the situation, because tax proposals that we’re hearing from Liz Truss aren’t going to help people like that.
"And I want to make sure that the people who really need our help do get the support they need to get through the winter.”
During a campaign visit to the West Midlands on Saturday, Ms Truss suggested her plans to halt "green levies" on energy bills, reverse the national insurance hike and implement supply-side reform could avert a downturn.
She told reporters: "What I'm about as a Conservative is people keeping more of their own money, growing the economy so we avoid a recession."
Ms Truss pointed the finger of blame at Mr Sunak's legacy as former chancellor, saying: "Under the plans at present, what we know is Britain is headed for a recession.
"That is not inevitable, but we need to avoid that by making sure our economy is competitive, that we're encouraging businesses to grow and that we are keeping taxes low.
"Having the highest taxes for 70 years is not going to deliver that economic growth and it's leading our country to a recession."
