Open warfare has broken out among Ukip's senior politicians after the party's only MP called on leader Nigel Farage to quit.
Douglas Carswell said the party needed a "fresh face" at the top but Mr Farage hit back, calling on the MP to "put up or shut up".
He said Mr Carswell was "out on a limb with almost no support in the party" and insisted his leadership enjoyed the "overwhelming" backing of the party's voters.
Mr Carswell's attack on the leader was motivated by the party's poor result in the Oldham West and Royton by-election, which saw Labour comfortably hold the seat with a majority of more than 10,000.
In an interview with BBC Essex, Clacton MP Mr Carswell said: "The Oldham by-election to me said very clearly that I think we need a fresh face."
Mr Carswell suggested that Mr Farage had taken the party as far as he could and Ukip needed to "change gear".
He said: "We all need to think very carefully as to whether or not we can build beyond the base we have now got without that change.
"We have gone from being a party with 2%-3% market share to a party with 13%, 14%, 15% market share, and that's a phenomenal achievement , an incredible achievement and no one can ever say that that hasn't been an achievement.
"But sometimes a start-up needs to change gear and to change its management if it is to go to the next level."
He said the party should avoid being seen as "unpleasant" and "socially illiberal".
Instead, Mr Carswell suggested Ukip would make a breakthrough in the polls if it was an "optimistic, sunshine, smiley, socially liberal, unapologetically free market party".
But Mr Farage accused the Clacton MP of privately plotting against him since May's general election.
"He has been having a go at me every single day since the general election, it's just that he has been doing it in private, briefing members, officials or the press or anyone that cares to listen and I'm greatly relieved that today he said it in public," Mr Farage told Sky News.
"The message is simple: we are a very strongly united party. If you look at the national executive of Ukip, the MEP group of Ukip, I have got terrific support within the party.
"He is trying to sow division where none exists."
Mr Farage added: "Douglas, frankly, must put up or shut up."
Mr Carswell, who joined Ukip in a high-profile defection from the Tories, ruled himself out of running for the leadership, saying he did not have the "patience", but insisted he remained loyal to the party.
"I am 100% Ukip and I'm very committed to Ukip, I'm not going anywhere," he said.
Mr Farage said the MP must "either accept the course that Ukip is going on, accept that we are united, accept our policy platform".
He defended the party's focus on controlling immigration and "clearly on issues like this, Douglas Carswell has different priorities".
"If Douglas finds it difficult, if Douglas finds it uncomfortable to talk about these issues, like open-door immigration, well I'm sorry but that's who we are."
Mr Farage said an opinion poll had indicated 91.4% of Ukip voters backed his leadership: "That is pretty overwhelming."
MEPs rallied around Mr Farage, with Ukip's deputy leader Paul Nuttall saying: "The Leave campaign needs a united Ukip. Nigel Farage has the support of the Ukip MEPs."
MEP Roger Helmer said: "I wish that Ukip's Westminster parliamentary party would focus on the big issue of Brexit, not navel-gazing about internal party issues."
James Carver, the party's Commonwealth spokesman, tweeted: "Furious with Douglas Carswell's snipe at Nigel Farage, reported to coincide with the EU summit. Douglas, you're wrong. Ukip backs Nigel."