The Tories can "kiss goodbye" to winning the next election if inflation is not brought under control quickly, Rishi Sunak has said.
Speaking at a leadership hustings in Eastbourne, the ex-chancellor, who wants to prioritise tackling rising prices before cutting taxes, seized on a warning by the Bank of England.
Rival Liz Truss said keeping taxes low was the best way to avoid a downturn.
She said the UK should not be "talking itself into a recession".
The Bank of England has warned inflation - currently 9.4% - could peak at more than 13% and stay at "very elevated levels" throughout much of next year, before eventually returning to its 2% target in 2024.
Ms Truss, who has promised to reverse some of Mr Sunaks tax rises, challenged the Banks gloomy economic prognosis, at the hustings.
But Mr Sunak highlighted its warning that inflation could become embedded, saying there would be "no hope that were going to win that next election" amid continuing rising prices.
Meanwhile, in an interview with the Financial Times, Ms Truss said people should be helped with the cost-of-living crisis by lower taxes, not giving "handouts".
She told the paper she would "look at what more can be done" but in a "Conservative way".
Mr Sunak and Ms Truss are vying for support from Conservative party members to be elected the next party leader, and prime minister.
Voting has started and the result is due to be announced on 5 September.
There was a brief disturbance at the hustings when Ms Trusss opening remarks were interrupted by a small group of climate activists, who were believed to be from the Green New Deal Rising group.
After the group was ejected from the event, Ms Truss took aim at what she called "unfair protests" that disrupted peoples lives.
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Watch: Protesters interrupt Liz Truss speech by delivering speeches of their own.
She pledged to clamp down on "militant people who try and disrupt our country" - mentioning both trade unions and environmental groups such as Extinction Rebellion.
Another protester was later removed from the event after interrupting Ms Truss.
Ms Truss, who will be attending the Commonwealth Games in Birmingham on Saturday, is also due to set out her proposals for boosting economic growth and levelling up the UK.
Her plans include reviewing the Treasury formula which determines which regional projects receive funding and creating "low-tax and low-regulation zones" across the country to create hubs for enterprise.
Elsewhere, Mr Sunak is vowing not to let "political correctness" stop him tackling "horrific" child grooming gangs, if he becomes leader.
In an interview due to be screened on GB News on Saturday, Mr Sunak said grooming gang members should face life sentences and that the police should record the ethnicity of those involved.
Mr Sunak said that as the father of two young daughters he believed there needs to be greater focus on tackling the crime.
A report published by the Independent Inquiry into Child Sex Abuse earlier this year recommended collecting ethnicity data of the victims and perpetrators of child sexual exploitation.
It said: "Many of the high-profile child sexual exploitation prosecutions have involved groups of men from minority ethnic communities.
"This has led to polarised debate about whether there is any link between ethnicity and child sexual exploitation networks.
"Poor or non-existent data collection makes it impossible to know whether any particular ethnic group is over-represented as perpetrators of child sexual exploitation by networks."
Mr Sunak told GB News "a particular group of people" were "perpetuating" child grooming and it was "far more pervasive across the country than actually we all realise".
He added: "And we all know the reason that people dont focus on it. Its because of political correctness and theyre scared of calling out the fact."
Separately, Mr Sunak is focusing on his opposition to another referendum on Scottish independence, warning in a statement issued by his leadership campaign that ignoring the SNP would be "dangerously complacent".
He said: "We cant just bury our heads in the sand and pretend they arent there - we need to stop them in their tracks."
His comment will be seen as a criticism of Ms Truss who earlier this week, said: "I think the best thing to do with Nicola Sturgeon is ignore her. "Shes an attention seeker, thats what she is."