Appearing before a Channel 4 studio audience, Ms Truss and Ms Badenoch accused Ms Mordaunt of having backed self-identification when she had responsibility for equalities issues – something she strongly denied.
The international trade minister said that while she had carried out a consultation of the Gender Recognition Act, she had never been in favour of self-ID.
“I can’t imagine why people are not comprehending what I say and have been regurgitating this issue for weeks and weeks,” she said.
“I’m a woman, I’m a biological woman in every cell in my body,” she said, adding that a man who had transitioned was “not the same as me”.
However, Ms Badenoch, the former equalities minister, said she found her rival’s account difficult to accept.
“When I took over equalities minister in 2020 what was being pushed was self-ID. I don’t understand how that would have changed unless someone else did it. My understanding was the previous minister who had the role had wanted (Ms Mordaunt) self-ID,” she said.
Ms Mordaunt retorted: “That is not correct. This will all be on record.”
However, Ms Truss, who also had responsibility for equalities alongside her role as Foreign Secretary, said there had been a plan to move forward on self-ID.
“I believe in women’s rights I also believe that transgender should be treated with respect, so I changed the outcome so we made the programme simpler and kinder, but not move ahead with self-ID,” she said.
Earlier, Ms Mordaunt said the attacks showed that she was the candidate to beat.
“I take it as a big fat compliment that nobody wants to run against me,” she said.
There were further clashes over tax as former chancellor Rishi Sunak defended his record in the Treasury as he attacked Mr Mordaunt and Ms Truss over their promised cuts.
Stressing the need to grip inflation, he said: “We cannot make it worse, inflation is the enemy that makes everyone poorer.
“I don’t think the responsible thing to do right now is launch into some unfunded spree of borrowing and more debt, that will just make inflation worse, it will make the problem longer.”
Ms Truss pinned the blame on the Bank of England, saying “we have inflation because of our monetary policy, that we haven’t been tough enough on the monetary supply, that’s the way that I would address that issue”.
Mr Sunak told her: “Borrowing your way out of inflation isn’t a plan, it’s a fairytale.”
Ms Truss responded: “I think it is wrong to put taxes up.”
The former chancellor then turned on Ms Mordaunt after she said her economic platform was not based on “tax and spend” but on “growth and competition”.
He said promises she had made to cut VAT on fuel and raise income tax thresholds would cost £15 billion.
“Even the pledges you’ve made are double-digit billion pound promises,” he told her.
“The best way to help everyone, the best way to make sure that they have money in their pocket, is to get a grip of inflation, and that should be everybody’s priority because that’s the thing that’s going to erode everyone’s living standards.”
Ms Mordaunt replied: “Two things, Rishi, that you haven’t realised – that is, I know you know people are going to need more help this autumn, but actually people need help now and you are going to have to do something on taxation.
“Next April we are going to be one of the most uncompetitive nations in terms of our tax competitiveness. That cannot be allowed to happen.”
Earlier, Tom Tugendhat sought to make a virtue of the fact that he was the only candidate without ministerial experience.
“We need a break from the Johnson years. That is why I am here. We need to make sure we can trust our politicians,” he said.
He drew applause from the audience when – alone among the candidates – he answered the question was Boris Johnson an “honest man” with the single word answer “No”.