The outgoing Prime Minister said a “huge amount” of help for households had already been promised and his successor – either Liz Truss or Rishi Sunak – would provide further support.
Regulator Ofgem has announced a rise in price cap for around 24 million households in England, Scotland and Wales, sending the average yearly bill from £1,971 to £3,549.
Mr Johnson highlighted the announcements already made which will see £1,200 going to the eight million most vulnerable households.
But he added: “Whichever of the two candidates gets in next week, what the Government is also going to do is provide a further package of support for helping people with the cost of energy.
“What we’ve got to do is get through the tough months – and I’m not going to shrink from this, it is going to be tough in the months to come, it’s going to be tough through to next year.”
The price increase in gas is being driven by Vladimir Putin’s invasion of Ukraine, he said during a visit to Dorset.
“We’re going to get through it,” Mr Johnson said. “We’re taking 26% more of our own gas from the North Sea than we did last year, we’re much less dependent on Putin’s supplies.”
He added “I just want to give people a sense of hope and perspective” because the UK was in a “strong economic position” which meant the Government had been able to provide support and it also had a “long-term British energy security strategy”.
The Prime Minister hinted at further announcements on nuclear power this week. He is understood to have given the go-ahead for financing for the construction of the Sizewell C nuclear reactor in Suffolk, although negotiations continue on the project.
Mr Johnson said: “We’re putting in more nuclear and you’ll be hearing more about that later this week. And we’re putting in absolutely shedloads of wind power as well.”
As the next prime minister will not take office until September 6, decisions on any further aid packages to help households struggling with soaring bills have been left to Mr Johnson’s successor.
Frontrunner Ms Truss’s camp said she will not finalise her plans for cost-of-living help before receiving the “full support and advice” only available to the government of the day.
Culture minister Matt Warman, a supporter of Mr Sunak, said blanket measures could be needed, with increased help targeted at those worst hit by the rise in energy bills.
He pointed to comments from Chancellor Nadhim Zahawi that suggested “this is something that is going to affect people somewhat higher up the income scale as well”.
He told Sky News that the principles of the earlier support package should remain in place to “focus the help on those who need it most but also to acknowledge that a degree of universality is the right one”.
Labour Party chairwoman Anneliese Dodds said the “massive increase” in the cap on energy bills “will plunge many, many households into financial distress” as she accused the Government of “fantasy economics” over the cost of living.
Asked about reports Ms Truss would support oil and gas drilling licences in the North Sea and if that is the answer, Ms Dodds told Times Radio: “No, it’s not, and the answer really is to be taking action to get the cost of those bills down.”
She added: “We are only ever going to be setting out plans that we have fully costed and I’m afraid right now from the Conservatives we’re just getting fantasy economics.
“They’re not saying how they would deliver anything. They keep changing their plans every five minutes. That’s not the case with Labour.”