The frontrunner in the race for the Ukip leadership, Paul Nuttall, admitted that the party has become "dysfunctional" as the four contenders to succeed Nigel Farage locked horns in their first broadcast debate.
Mr Nuttall warned that the eurosceptic party was "peering over the edge of a political cliff" and that he was the leader who could persuade it to "step back" rather than "step off".
All four contenders rejected former candidate Steven Woolfe's claim that the party is "ungovernable", but each acknowledged that changes were needed to bring an end to the factionalism seen in recent months.
Ex-deputy chair Suzanne Evans - who was suspended from the party earlier this year over remarks she made about Mr Farage - told LBC Radio: "Ungovernable? You just watch me. It's definitely not ungovernable."
Despite her previous rows with Mr Farage - and her criticism during the debate of his controversial Breaking Point poster as "insensitive and ill-judged" - Ms Evans said she would like the outgoing leader to act as "a kind of elder statesman figure to whom I can go and say `Nigel, what do you think of this?'"
Mr Nuttall insisted that his experience as Mr Farage's deputy leader made him the right person to unite the party, telling moderator Iain Dale: "We haven't covered ourselves in glory, not just over the past couple of months, but over the past year. Ukip has been dysfunctional.
"Ukip is peering over the edge of a political cliff and we will either step off or step back. I think I'm the person to make sure we don't step off that political cliff."
London Assembly member Peter Whittle said the party needed "a period of stability", adding: "My temperament is a stable one, I don't search for conflict."
And former parliamentary candidate John Rees-Evans said the party needed "major reform", with members allowed to decide policies for the manifesto.
Mr Rees-Evans said he was running for the leadership because people like Ms Evans, who wrote the 2015 Ukip manifesto, "think they know better than ordinary people".
And he accused her of trying to"trash the reputation" of Christian campaigner Alan Craig, whose selection as a Ukip candidate caused controversy over alleged homophobia following his comments about "gay rights stormtroopers".
Describing Ukip as a libertarian party, Mr Rees-Evans said it was "not acceptable" for Ms Evans to seek to bar a candidate for having "traditional views". But Ms Evans insisted that as leader: "I will not tolerate racism, I will not tolerate homophobia, I will not tolerate discrimination".
While Ms Evans said she was "vehemently opposed" to the death penalty, and Mr Whittle said he did not support it, Mr Nuttall said he backed its reintroduction for child killers and Mr Rees-Evans said he would bring it back for paedophiles and child murderers.
Challenged over whether all paedophiles should be executed, Mr Rees-Evans said "Yes", before adding that he would not necessarily impose the death penalty in cases involving "someone who looked 18 and was 15 and a half".
"It obviously depends what you define as a paedophile," he said. "I would have the death penalty for somebody who is (targeting) pre-pubescent (children)."
The candidates were confronted by a Spanish national named Maria who had been a long-term resident of the UK but had faced verbal abuse since the referendum vote.
Mr Nuttall told her: "I'm very sorry if you were verbally abused, no-one should have to go through that, but the bottom line is this - I don't feel responsible because Brexit is great."
Mr Whittle said that "a huge amount" of the hate crime reported following the June 23 referendum was related to anger about terrorism, but Maria responded that her abusers had mentioned the Europe issue, telling the Ukip politicians: "You created a war." Mr Whittle responded: "This is ridiculous. We didn't create a war."
Mr Rees-Evans accused Mr Nuttall and Ms Evans of seeking to "shunt Nigel (Farage) off into the political graveyard that is the House of Lords" to keep him out of the Ukip frontline.
But Mr Nuttall insisted: "I think it would be fitting that Nigel becomes the honorary president of the party and - if he wants it - a peerage should be on the cards."
Ms Evans refused to say who she wanted to win the US presidential election and Mr Nuttall said he would vote for Libertarian candidate Gary Johnson. Mr Rees-Evans said he was concerned about revelations about both candidates, but would say in Donald Trump's favour that he was "not in anyone's pocket".
Mr Whittle said: "Hillary (Clinton) is a deeply unsavoury character, like Putin. With Trump, my feeling is `Right cause, wrong man'."