Tory leadership rivals Boris Johnson and Jeremy Hunt are at loggerheads over how the UK should leave the EU.
Both contenders for prime minister claim they can renegotiate a Brexit deal that the EU says is closed.Mr Johnson said the UK must leave on 31 October "deal or no deal" but Mr Hunt called this a "fake deadline" that could trigger a general election if Parliament rejects a no-deal Brexit.
The winner of the contest will take over from Theresa May on 24 July.
In an interview with Talk Radio, Mr Johnson insisted he would take the UK out of the EU by Halloween "come what may, do or die" and has challenged his opponent to make the same commitment.
Mr Hunt said he would leave the EU without a deal, but not if there was a "prospect of a better deal".
It comes as International Trade Secretary Liam Fox - who is backing Mr Hunt - again criticised Mr Johnson's claim that the UK could continue tariff-free trade with the EU in the event of a no-deal Brexit.