Mr Hunt and fellow contenders Michael Gove, Dominic Raab, Sajid Javid and Rory Stewart faced questions from host Krishnan Guru-Murthy and a studio audience in the 90-minute Channel 4 broadcast on Sunday evening.
Channel 4 installed an empty podium on the stage in place of Mr Johnson, who declined the invitation.
During the debate, Mr Hunt asked: “Where is Boris? If his team won’t allow him out with five fairly friendly colleagues, how is is he going to deal with 27 European countries?”
The programme also saw some tense exchanges over Mr Raab’s insistence that suspending parliament to force through Brexit should remain on the table.
“I don’t think it is likely but it is not illegal,” he said.
International development secretary Mr Stewart warned shutting down parliament would “undemocratic” and “deeply disturbing”, while Mr Javid likened the strategy to that of a “dictator”.
Here’s how we covered the debate as it happened.
Good evening and welcome to The Independent's live coverage of the first televised debate between the Conservative leadership candidates.
Jeremy Hunt, Michael Gove, Dominic Raab, Savid Javid and Rory Stewart will be setting out their stalls on Channel 4 in just over half an hour as they seek to gain ground on Boris Johnson, the strong favourite to replace Theresa May.
Johnson himself will be conspicuous by his absence, having declined the invitation as he keeps a low media profile in the run-up to next week's votes.
Tonight's proceedings - overseen by Krishnan Guru-Murthy - will get underway at 6.30pm.
Boris Johnson has an "open invitation" to join his leadership rivals at this evening's debate, host Krishnan Guru-Murthy has tweeted:
The leadership candidates have arrived in Stratford, east London, ahead of the debate.
Underdog Rory Stewart, speaking as he entered the studio, said he was "looking forward'' to the debate and hoped that Boris Johnson was going to "make a last-minute appearance''.
He added: "We're choosing a prime minister and the public has the right to hear from us and judge who had the qualities to be prime minister Minister.''
Stewart said he was hoping to discuss "what we can achieve after Brexit, the way we can make this country fairer, greener, and more united'' during the live debate.
Michael Gove told journalists outside the studio he was "looking forward to a positive exchange''.
"There's still time for Boris to get a taxi from north London," jokes Krishnan Guru-Murthy as he previews the debate on Channel 4 News.
We're underway on Channel 4, where Krishnan Guru-Murthy is introducing each of the candidates (who have turned up) ahead of a 90-minute debate.
Boris Johnson is welcome to join them at any point, he says.
Krishnan Guru-Murthy takes the first question from the audience: How do you intend to defeat Corbyn and Farage?
Michael Gove is the first to answer: "There is nothing more important than preventing Jeremy Corbyn getting into Parliament."
He says the party needs "someone who has strong beliefs in Conservative principles" and said Corbyn would push "Marxist economics".
Gove provokes laughter among the audience by suggesting Corbyn would be "the most terrified" of him out of all of the candidates.
Jeremy Hunt says the only way to beat the Brexit Party is to deliver Brexit.
Corbyn "is against aspiration, he is against British values, he is against Britain", he claims.
"We will only get a majority if we reach out to the centre ground", he says, adding the party needs to win over young people who have not voted Tory.
Here's the scene in the studio, where an empty podium reserved for Boris Johnson is conspicuously placed at centre stage, between Sajid Javid and Dominic Raab.
The audience is made up of "floating voters" willing to choose the Tories at an election.
There's the first moment of tension between the candidates as Rory Stewart and Dominic Raab clash a prime minister suspending parliament to force through Brexit.
Asked if he would be willing to do it, Raab says it is unlikely to happen would not be illegal.
Stewart says Raab will not take it off the table as he knows there there is no way of getting his Brexit deal unless he suspends parliament.
That’s “nonsense”, says Raab, who accuses his rival of misrepresenting him.
Jeremy Hunt says shutting parliament would be a "profound mistake" and "wrong" and Sajid Javid also ruled it out as undemocratic.
"We are not selecting a dictator of our democracy," Javid says.
Stewart also says proroguing parliament would be "undemocratic" and "strike at the heart of our constitution".
"They think they are threatening something but a threat is not credible unless it can be delivered," he adds, accusing his rival candidates of taking part in a "competition of machismo".
Next question from the audience: how can you seriously contemplate a no-deal Brexit?
Jeremy Hunt launches the first attack on Boris Johnson, who he says should be here to answer that question.
He says no-deal needs to stay on the table in case it turns out to be the only way of delivering Brexit. But he says he would only allow the UK to crash out of the EU "with a heavy heart".
Michael Gove says no one wants a no-deal Brexit, but he would always choose that option over remaining in the EU after the UK voted to leave.
Krishnan Guru-Murthy ask Michael Gove why the EU would be willing to renegotiate the withdrawal agreement for him as prime minister, when they would not for Theresa May.
Gove says he is used to overcoming "impossible odds", but doesn't really answer the question.
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