The Conservatives face “potential extinction” if they do not get Brexit done, Boris Johnson has warned.
The former foreign secretary told a leadership hustings the party will “not be forgiven” if it does not take the UK of the EU by the 31 October deadline.
He said he was best placed to beat Labour and “put Nigel Farage back in his box” but reportedly ruled out a snap general election if he becomes PM.
Mr Johnson is one of 11 candidates vying to succeed Theresa May as leader.
On Tuesday, two candidates pulled out of the leadership race as the party tightened the rules for the contest amid concerns about the size of the field.
Mr Johnson, Home Secretary Sajid Javid, International Development Secretary Rory Stewart and ex-Commons leader Andrea Leadsom addressed the One Nation Conservative Caucus of Tory MPs in Parliament at the first hustings of the campaign.
The group, which opposes a no-deal Brexit, has invited all the candidates to appear before them to make their case for the top job.
Mrs Johnson, regarded as the frontrunner in the contest, said the party was facing an “existential crisis” following its drubbing in last month’s European elections.
“We will not be forgiven if we do not deliver Brexit on October 31,” he said.
“We need to realise the depth of the problems we face. Unless we get on and do this thing, we will be punished for a very long time. There is a very real choice between getting Brexit done and the potential extinction of this great party.”
He suggested the solution to the current deadlock would be to replace the Irish backstop – the controversial insurance policy designed to maintain an open border – with “alternative arrangements” so as to facilitate a “managed exit” from the EU.
The EU has said the backstop must remain in the withdrawal agreement and has resisted calls from Tories and the DUP for a time limit, or exit date, to be put on it.
The Tory leadership hustings hosted by the One Nation Caucus of Conservative MPs began with reporters, me included, starting to loiter outside.
Between us and the action inside, there were two heavy wooden doors and a pretty thick wall – and some parliamentary security staff not particularly keen on us leaning too obviously against either the doors or the wall.
A rather forthright conversation then began between us lot in the press pack and Conservative Party officials about why we weren’t allowed in – given those in the room were discussing who should be our prime minister by the end of next month.
Mr Johnson, who has insisted the UK must leave by the end of October with or without a deal, said a no-deal exit would cause “some disruption”.
But he warned that demands for another referendum on the UK’s future in Europe would grow if the UK was forced to seek another extension from the EU.
He insisted: “I believe I am best placed to lift this party, beat Jeremy Corbyn and excite people about conservatism and conservative values.”
Home Secretary Sajid Javid told the meeting that if his party “don’t look like change, voters will go for change in the form of (Jeremy) Corbyn”.
He stressed that the party should not seek to emulate Nigel Farage’s Brexit Party, insisting “we will not beat the Brexit Party by becoming the Brexit Party”.
In a reference to Benjamin Disraeli’s “one nation” political philosophy, he added: “One nation is a term that was coined by a prime minister who was a bit of an outsider. Pick a prime minister who is also a bit of an outsider.”
International Development Secretary Rory Stewart told MPs he would not sign a confidence and supply deal with the DUP in exchange for funding, as Mrs May did.