Suzanne Evans and Paul Nuttall have both announced they will stand to be leader of Ukip.
Nuttall, the former deputy leader of the party who is seen as a threat to Labour in the north of England, said he would be the “unity” candidate.
While Evans, the former deputy chairman who may appeal more to Tory voters in the south, said she wanted to stop the party moving to the “far right”.
Yesterday, Ukip’s most high-profile donor, Arron Banks, backed Raheem Kassam, a former aide to Nigel Farage, for the leadership.
Nuttall told the BBC’s Sunday Politics today that Ukip was “facing an existential crisis” following the Brexit result. “Ukip at the moment is looking over the edge of a political cliff, it will either step off or it will step back,” he said.
“We have to move beyond Nigel Farage, we have to build sensible structures within the party,” he said. I think I’m the only person who can keep Ukip in the game.”
Earlier in the morning, Evans announced she would seek to replace Farage while speaking on the BBC’s Andrew Marr programme.
“I think I am the right person to lead Ukip into the challenges ahead, to be able to beat the first-past-the-post system by broadening our appeal,” she said.
Over the past year, Evans has been sacked by Farage from multiple jobs in Ukip amid fierce internal battles over the future direction of the party.
Evans said today Kassam would try and copy Donald Trump if he won the leadership. “I don’t think there is any doubt about that. Our members don’t want that,” she said.
“Our future as a political party in Britain does not lie in that far right wing,” she said. “I do not see a groundswell of opinion for more far right policies.”
“I think I am absolutely the right person to champion the cause of those 17.4 million people who voted to leave the EU and are now seeing their democratic choice being undermined by the political class.”
Evans said Ukip needed to shed the “toxic” image it had among many voters.
Responding, Farage said Evans was wrong to begin her leadership campaign by “decrying” Kassam. “I won’t be voting for her,” he told ITV’s Peston on Sunday.
The present leadership contest was triggered when Diane James quit after just 18 days in charge and has been thrown wide open after frontrunner Steven Woolfe quit in the wake of an altercation with a fellow MEP.
Kassam, an ex-chief of staff to Farage, welcomed the support offered by Banks, the co-founder of the Leave.EU Brexit campaign.
He said: “This is a major endorsement from someone who has been one of the driving forces behind Ukip in recent years.
“Mr Banks ploughed his personal time and money into the referendum campaign and the party, and for those wondering whether he still stood with Ukip, this is a very clear sign: he does, under a Kassam leadership.
“I’d like to thank Arron for the brave and important support, and I look forward to working with him to make Ukip great again.”
Banks said on Twitter: “I’ve been very impressed with Raheem’s ideas, despite Paul Nuttall running I think he’s the candidate to beat. He’s got my support.”
The new Ukip leader will be announced on November 28, with nominations to replace Ms James closing on October 31.