Jeremy Hunt has goaded Boris Johnson for pulling out of a television debate as the Tory leadership candidates hit the campaign trail hard.
Meanwhile, Mr Hunt said he would instead hold a question-and-answer session on Twitter.
Earlier, Mr Johnson again declined to discuss in detail a late-night quarrel at his home, saying it was “simply unfair” to “drag” his loved ones into the political arena in an interview with the BBC.
After Mr Hunt accused him of ducking public scrutiny, Mr Johnson has a flurry of broadcast interviews and visits in the south east planned for Tuesday.
A spokesman from his camp claimed: “We’re definitely stepping it up.”
After days avoiding journalists’ questions, the former foreign secretary sought to get his campaign back on track, declaring he would deliver Brexit by the Halloween deadline “do or die”.
Mr Hunt, meanwhile, hit back at his rival, dismissing 31 October as a “fake deadline” which would more likely result in a general election which could hand the keys of No 10 to Jeremy Corbyn.
The foreign secretary suggested Mr Johnson would be unable to win the trust of other EU leaders to successfully negotiate a new Brexit deal with Brussels.
In a letter to his rival, Mr Johnson said the “central question” in the leadership contest was the issue of whether the next prime minister would commit to leaving the EU by 31 October.
“If we fail to deliver once again, the consequences for our party and our country will be devastating,” he said. “We must not kick the can down the road again. The British people have had enough of being left in limbo.”
Follow how the day in Westminster unfolded
Frontrunner Boris Johnson has been warned that as many as a dozen Tory MPs are ready to back a vote of no confidence, triggering a general election, to stop a no deal Brexit.
Here’s our political editor Andrew Woodcock with all the details.
Boris Johnson warned Tory MPs will back vote of no confidence to block no-deal Brexit
Jeremy Hunt tells his rival for prime minister to ‘man up’ and face him in live TV debatesIf you missed his interview with the BBC’s Laura Kuenssberg, Boris Johnson again declined to discuss in detail a late-night quarrel at his home, saying it was “simply unfair” to “drag” his loved ones into the political arena.
Asked what happened that night by Kuenssberg, Mr Johnson said he did not want to “drag” his family and loved ones into the political spotlight.
He said: “I... would love to tell you about all sorts of things, Laura, but I’ve made it a rule over many, many years - and I think you’ve interviewed me loads of times - I do not talk about stuff involving my family, my loved ones.
“And there’s a very good reason for that. That is that, if you do, you drag them into things that... in a way that is not fair on them.”
The Tory leadership frontrunner also called for “creative ambiguity” over the £39 billion cost of the UK’s Brexit divorce deal.
Boris Johnson has been warned that as many as a dozen Conservative MPs will back a vote of no confidence, triggering a general election, to block a no-deal Brexit, writes political editor Andrew Woodcock.
The former foreign secretary has promised to take the UK out of the Europe Union on 31 October with or without an agreement on divorce terms.
And his rival for the Tory leadership, Jeremy Hunt, the current foreign secretary, has not ruled out a potentially damaging no-deal outcome, though he says he is ready to extend Brexit negotiations in the hope of avoiding it.
With the incoming prime minister likely to have a working majority of no more than three MPs in the House of Commons when he arrives at 10 Downing Street next month, the defence minister Tobias Ellwood left no doubt that opponents of no deal believe they have the numbers to stop the UK crashing out.
“I think a dozen or so members of parliament would be on our side, would be voting against supporting a no deal, and that would include ministers as well as backbenchers,” he told BBC1’s Panorama: The Race for Number 10.
Hopes that a change in position would be agreed on Tuesday at a crunch shadow cabinet meeting were dashed after the union’s intervention in talks with Jeremy Corbyn.
Senior shadow cabinet ministers including Tom Watson, the deputy leader and Sir Keir Starmer, the shadow Brexit secretary, will continue to press for full-throated support for a Final Say vote, but now believe they will have to wait longer for a breakthrough.
Boris Johnson, the leadership contender, is now appearing on LBC Radio. According to the Press Association he dodged waiting journalists as he arrived at the studios.
The front-runner to become the next prime minister was driven past a group of photographers and reporters into a private car park beneath the Global radio office in Leicester Square.
Boris Johnson has refused to deny that a photo of him apparently making up with his girlfriend Carrie Symonds was staged.
The Tory leadership favourite blocked multiple questions about whether he knew how the snap, of the pair in the Sussex countryside, ended up in newspapers.
He claimed that "politics has totally changed" since March 29 and "we are staring down the barrel of defeat".
He told LBC: "People are looking at this thing and thinking 'Parliament is just not going to do this'.
"But, actually, I think they are."
Boris Johnson’s constituents have said he should “face the music” and take part in a live TV debate so the public can hear what he has to say if he wants to become prime minister.
The Tory leadership frontrunner was branded a “bottler” and a “coward” by opponent Jeremy Hunt for refusing to face scrutiny after Sky News was forced to cancel a debate between the pair.
The former foreign secretary has faced mounting pressure to answer questions about the police being called to the Camberwell home he shares with girlfriend Carrie Symonds after a loud late-night altercation.
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