During the Channel 4 programme, the five remaining candidates were asked by host Krishnan Guru-Murphy to give a yes or no answer to the question.
Penny Mordaunt said: “I'm not doing a yes or no because I think it would be wrong to do that. There have been some really severe issues and I think he has paid a price for that.”
Liz Truss said Mr Johnson had "been very clear himself that he made mistakes in government” but she had taken his explanation for inaccurate statements over partygate “at face value”.
Frontrunner Rishi Sunak said he had tried to give the PM the benefit of the doubt for "as long as possible".
"Ultimately, I reached the conclusion that I couldn’t, and that’s why I resigned… There were a number of reasons that I resigned but trust and honesty was part of that,” he continued.
When asked to explain why it would be okay to have a prime minister who has broken Covid-19 rules, after being fined by the Met Police for attending a birthday party for the PM at Downing Street, Mr Sunak said it was a "mistake" and reiterated his apology.
Though he regretted breaking Covid-19 laws, he said the reason he was in the Cabinet room for the gathering was because he was there working "every day" on coronavirus, but added: "I wish it had never happened."
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Meanwhile, the rivals clashed over their tax plans - a running issue throughout the leadership race so far as the cost of living crisis deepens.
Former chancellor Mr Sunak, who resigned last week, defended his record in the Treasury as he attacked Ms 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.”
But Ms Truss retorted "you can't tax your way to growth" and it's "wrong to put taxes up".
Mr Sunak insisted he had made the right decisions during his time in the Treasury - such as raising National Insurance to plug gaps in health and social care funding - and told his rivals that promising tax cuts now and "borrowing your way out of inflation isn't a plan, it's a fairytale".
Mr Sunak hit out at Mr Tugendhat for voting against him when he proposed raising National Insurance to help tackle the NHS's record backlog - but his opponent claimed Mr Sunak only supported the tax hike because Mr Johnson had ordered it.
"I asked why on Earth this was going to be necessary and you told me: 'because the boss wanted it'," Mr Tugendhat claimed.
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.
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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.”
Responding to the debate, Labour’s Shadow Chief Secretary to the Treasury, Pat McFadden, said the UK "doesn’t need another prime minister incapable of being straight with the British public".
"But the Tory wannabes all lined up to offer billions of pounds of unfunded tax cuts without saying whether the money would come from more borrowing or more cuts to public services,” he added.
Row over transgender rights
Ms Mordaunt also came under attack for her record on transgender issues, with Ms Truss and Ms Badenoch saying she had pursued a policy of gender self-identification when she had responsibility for equalities issues. She strongly denied this.
Frontrunners Ms Mordaunt said the attacks showed she was the candidate to beat after she finished an unexpectedly strong second in the first two rounds of voting by MPs.
“I take it as a big fat compliment that no-one wants to run against me,” she said.
Ms Truss, who is seeking to overhaul Ms Mordaunt to secure a place in the final ballot of party members, insisted she was running an “entirely positive” campaign.
She nevertheless joined Ms Badenoch in questioning Ms Mordaunt’s account of her record on gender self-identification in the first flashpoint of the evening.
“I can’t imagine why people are not comprehending what I say and have been regurgitating this issue for weeks and weeks,” Ms Mordaunt said.
“I’m a woman, I’m a biological woman in every cell in my body,” she said, adding that a man who had legally transitioned was “not the same as me”.
Ms Badenoch, who took over as equalities minister in 2020, said she found her account “difficult” to accept as the policy that was being pushed at that time was self-identification.
“So, I don’t understand how that would have changed unless someone else did it in between,” she said.
“I didn’t work with Penny, but my understanding was that the previous minister who had done the role had wanted self-ID, and that was something that I reversed with Liz.”
Ms Mordaunt retorted, saying “that is not correct and this will all be on record in government" - to which Ms Badenoch replied: “It is on record.”
She was backed by Ms Truss, who also has responsibility for equalities alongside foreign policy, who also said there had been a plan to move forward on self-identification.
Earlier, Mr Tugendhat sought to make a virtue of the fact that he was the only candidate in the race 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.
The word “Dumbledore” was soon trending on Twitter when the former military officer quoted JK Rowling’s character from her beloved Harry Potter series after being asked by an audience member: “Why should the public trust you?”
Mr Tugendhat echoed the famous wizard’s sentiment when he told the debate: “It’s easy to stand up to your enemies – it’s sometimes harder to stand up to your friends.”
He spoke while acknowledging “trust in politics has been collapsing, trust in our party has been collapsing”, and added: “I’ve been holding a mirror to many of our actions and asking those in our party, those in our leadership positions, to ask themselves ‘is that what the public really expects?’
“Are you serving the people of the United Kingdom or are you serving your career? Because that’s the real question tonight. That’s the real question for all of us.”
The Channel 4 leadership debate was the first amid this year's contest.
ITV will host the second on Sunday at 7pm. It can be watched live or on catch-up on ITV Hub.