Boris Johnson has challenged Jeremy Hunt, his rival for the Tory leadership, to commit to taking Britain out of the EU by the end of October.
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".
However he continued to avoid questions about his personal life as he returned to the campaign trail following a late-night row with partner Carrie Symonds that saw police called to their home last week.
Hunt, meanwhile, hit back at his rival, dismissing October 31 as a "fake deadline" that would more likely result in a general election which could hand the keys of No 10 to Jeremy Corbyn.
The foreign secretary suggested 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, 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 October 31.
But in a BBC interview, Hunt warned that insisting upon the October 31 departure date was a mistake.
While he said that getting a new deal by the end of October was "doable", it required a prime minister who the other EU leaders trusted and were prepared to talk to.
"It's about the personality of our PM. If you choose someone where there's no trust, there's going to be no negotiation, no deal," he said.
Johnson used a series of broadcast interviews to set out his plans for Brexit, insisting that the shock of the European election results would force both the Tories and Labour to acknowledge that the current impasse could not continue.
He will find out whether he has achieved his ambition of becoming Tory leader when the results of the contest are announced on July 23 under the timetable set out by the Conservative Party.
Johnson told TalkRadio the UK would be leaving the EU on October 31 "do or die, come what may".
But he could not escape continued questions about his private life after the events in the early hours of Friday morning when police were called to his home by neighbours.
On LBC Radio, he was repeatedly challenged about whether his campaign was behind the release of a picture of him with Symonds in an attempt to show their relationship was going strong.
Asked where the photograph had come from, Johnson said: "The longer we spend on things extraneous to what I want to do... the bigger the waste of time."
When host Nick Ferrari suggested his hairstyle indicated it was an old picture, he said: "This conversation is now descending into farce."
Turning to Brexit, Johnson said "politics has totally changed" since March 29 and "we are staring down the barrel of defeat" which would focus minds in parliament.
Hunt said that he believed it would become clear "well before" October 31 if it was possible to get a new deal with the EU.
"If there isn't and if no deal is still on the table I've been very clear. I will leave the European Union without a deal," he said.
"But I'm not going to do that if there's a prospect of a better deal and if I did it it would be with a heavy heart because businesses up and down the country would face a lot of disruption."
Australian Associated Press