Dominic Raab has been making his pitch to become Conservative leader, as Michael Gove becomes the eighth MP to join the race to succeed Theresa May.
Mr Raab told the BBC he would fight for a “fairer” Brexit deal with the EU – but if that were not possible, the UK would leave with no deal in October.
Mr Gove confirmed he would run to “deliver Brexit” and unite the party.
Chancellor Philip Hammond said it would be a “dangerous strategy” to ignore Parliament, which has opposed no-deal.
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On Friday, Mrs May announced she would be standing down as Tory leader on 7 June, saying it was time for another prime minister to try to deliver Brexit.
It came after a backlash by her MPs against her plan to get the withdrawal deal she had negotiated with the EU through the Commons, which has already rejected it three times.
The UK is now set to leave the European Union on 31 October, after the original Brexit date of 29 March was delayed twice owing to the parliamentary deadlock.
The delay has meant the UK has had to take part in elections to the European Parliament, three years after it voted to leave the bloc.
Mr Gove, the environment secretary, confirmed on Sunday that he would run for leader, saying: “I believe that I’m ready to unite the Conservative and Unionist Party, ready to deliver Brexit, and ready to lead this great country.”
Speaking to Nick Robinson for BBC Radio 4 podcast Political Thinking at Hay Festival, Mr Gove explained why he was running, saying: “The particular mix of experience I have means I can make a contribution.”
Mr Gove also said he had changed his mind from 2016 – when he described himself as being “incapable” of being Tory leader – adding he had “evolved as a politician”.
While he did not set out his leadership proposal, he did say that the future prime minister would need an eye for detail, as the “process for taking us out of the European Union requires that”.
Former Brexit Secretary Dominic Raab and former Commons leader Andrea Leadsom revealed their leadership bids in the Sunday newspapers.
Mr Raab told the BBC’s Andrew Marr Show that the UK’s previous negotiations with the EU over the withdrawal agreement had not been “resolute” enough, and a no-deal Brexit had been taken “off the table”.