Rishi Sunak and Liz Truss have pulled out of Tuesday's leadership debate amid fears previous clashes have seriously damaged the Tories.
Sky News confirmed it would cancel the clash after the two candidates said they didn't want to take part.
Sources on both campaigns admitted they did not want to go ahead with the third TV debate after ripping each other to shreds on ITV and Channel 4 over the weekend.
They fear the bitter 'blue on blue' action would be a further blow to the Tories' standing when the country is struggling through a cost of living crisis.
Both camps suggested they wanted to focus on MPs' hustings in the run-up to the final vote on Wednesday.
Labour said the leadership contest had become so "embarrassing" that the debate was axed to stop the public seeing candidates "fighting like rats in a sack".
A source in Team Sunak suggested it had never firmly committed to the Sky debate.
"We are very happy to do more debates if we are lucky enough to get to the next stage, including Sky News," a source told the Mirror.
"We've done two in the last three days which I think is enough at this stage."
A Team Truss source said: "It is not the right time to be doing more debates when this part of the contest only has 358 voters. The C4 debate in particular was a massive mistake and candidates were wrong to take part in it."
Contenders for the Tory leadership will be whittled down to just four later today as MPs cast their votes in the third round of the contest to find a successor to Boris Johnson.
The ex-Chancellor and Foreign Secretary clashed during Sunday's ITV debate with Ms Truss criticising Mr Sunak for putting up taxes to their highest level in 70 years, choking off economic recovery in the process.
Mr Sunak hit back, accusing her of peddling "something-for-nothing economics", adding that "isn't Conservative. It's socialism".
He later asked her pointedly which she regretted most - having been a Remainer or a Lib Dem.
In response, she attacked his elite schooling.
Sources told the Times that at the end of Friday's vitriolic leadership debate on Channel 4, Mr Sunak turned to Ms Truss and asked: "Why are we doing this?"
Both have questioned the point of the debates amid concerns about where they will leave the Conservative Party in the long-term.
Deputy Labour leader Angela Rayner said: "The country deserves better than Tory candidates hiding from scrutiny simply because their first two performances have shown they would be a danger to the economy and the future of the UK.
“This is a hopelessly divided Tory party, one that has racked up over £300 billion in unfunded promises and yet still has no plan to get to grips with their cost of living crisis. Only a Labour government can give Britain the fresh start it needs.”
“This Conservative ‘leadership’ contest is so embarrassing they’ve cancelled the debate - so you can’t see them fighting like rats in a sack.”
Tory infighting has become increasingly bitter, with Penny Mordaunt's departmental boss accusing her of missing meetings to plot her leadership bid.
International Trade Secretary Anne-Marie Trevelyan told LBC that colleagues had been left to pick up the pieces when Ms Mordaunt wasn't there.
She said: "We all do our jobs in different ways.
"Understandably, perhaps, now it's clear, Penny has for the last few months spent some of her time focused on preparing her leadership campaign, for which I have utmost respect, that's how this system works."
