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 out of the EU by 31 October as planned, BBC reports.
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.
His comments came as the Eurosceptic European Research Group (ERG) called on leadership contenders to abandon Mrs May's Brexit deal.
A paper published by the influential ERG said the next prime minister should sign up to the 31 October deadline and step up preparations for a no-deal exit on World Trade Organisation terms.
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, 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."
His warning was echoed by fellow leadership hopeful Ms Leadsom, who said a delay to the UK's exit from the EU could "spell the end" for the party.