Pair clashed in second debate of the contest on Sunday evening
It comes after the pair clashed in the second televised debate of the contest last night, with the former chancellor accusing the foreign secretary of offering “socialist” proposals in her bid to succeed Boris Johnson in No 10.
In the heated exchanges, Ms Truss also accused her former cabinet colleague of risking recession, adding: “Rishi, you have raised taxes to the highest levels in 70 years. That is not going to drive economic growth”.
A source in Mr Sunak’s campaign told The Independent he would not take part in Tuesday’s debate, adding: “We are very happy to do more debates if we are lucky enough to get to the next stage, including Sky News”.
It is also understood Ms Truss had made clear she would only participate in the debate if all candidates have committed to doing so.
In respsonse, the broadcaster said the event has been cancelled, saying: “Two of the three candidates currently leading in the MPs’ ballot – Rishi Sunak and Liz Truss – have confirmed to Sky News that they do not want to take part”.
“Conservative MPs are said to be concerned about the damage the debates are doing to the image of the Conservative Party, exposing disagreements and splits within the party.
“Both are very welcome to taking part in future Sky News televised debates.”
The leadership contenders – Mr Sunak, Ms Truss, Penny Mordaunt, Tom Tugendhat and Kemi Badenoch – have already taken part in debates on Channel 4 and ITV which have seen the would-be prime ministers taking primetime pot shots at each other.
In response to the decision by Sky News to cancel the debate, Penny Mordaunt’s campaign team said: “Throughout this contest she has never dodged media or shied away from broadcast interviews and debates – people deserve to hear from their leaders.
“Its a shame some colleagues cannot find a way to debate one another in a civil way. Last night Penny showed she is the only candidate with a plan to unite the party, defeat Labour and lead the country forward”.
The Labour leader Sir Keir Starmer also said he was “astonished” by the candidates withdrawing from a televised debate, saying it demonstrated a lack of “confidence”.
He said: “I’m astonished that those that want to be prime minister of the United Kingdom are pulling out of debates and out of scrutiny.
“I can see based on what I’ve seen in the debates so far why they want to do so because this is a party that is out of ideas, out of purpose, they’re tearing each other apart.”
On Monday MPs in the Conservative Party are set to hold a third ballot in the Tory leadership contest, eliminating one more contender with the smallest number of votes. By Wednesday the candidates will be whittled down to two that will face a vote of the Tory membership over the summer.