Former cabinet members Dominic Raab and Andrea Leadsom are the latest Tory MPs to announce they will run for party leader.
They become the sixth and seventh candidates to enter the race after Theresa May said she would resign as party leader on 7 June.Speaking to the Mail on Sunday, Mr Raab said the UK needed to leave the EU on October 31 "at the latest".
Ms Leadsom said she also supported a no-deal Brexit "if necessary".
The former Commons leader and Environment Secretary told the Sunday Times to "succeed in a negotiation, you have to be prepared to walk away."
Mr Raab - Mrs May's Brexit Secretary before he resigned in November 2018 - said he would "prefer" a deal but he said the country needed to "demonstrate unflinching resolve" to leave when negotiations end in October.
Environment secretary, Michael Gove is also set to announce he will contend for the leadership role, according to the Sunday Times.
Mrs May will continue as prime minister while the leadership contest takes place.Five other candidates have so far confirmed their intention to stand:
Foreign Secretary Jeremy Hunt
International Development Secretary Rory Stewart
Health Secretary Matt Hancock
Former Foreign Secretary Boris Johnson
Former Work and Pensions Secretary Esther McVey