Frontrunner Boris Johnson and Home Secretary Sajid Javid were the final two of the 10 candidates to launch their campaigns, as the battle for Number 10 intensifies.
"I am not aiming for a no-deal outcome", Johnson, a 54-year-old former foreign minister and London mayor, said.
But he said the threat of no deal was a "vital" negotiation tool and the United Kingdom "must do better" than the current deal.
However, Rory Stewart has dismissed the idea of negotiating a better deal as "a fairy story", while finance minister Philip Hammond dismissed an October Brexit as "impossible".
Johnson has won over many in his party by arguing that only he can rescue the Conservatives, who have been punished in recent elections over the government's inability to deliver Brexit on time.
Theresa May announced her resignation as prime minister last month, bowing to pressure from her own party amid growing anger over her inability to push through a favorable Brexit deal with the EU.
"I am the change candidate, Boris Johnson is yesterday's news", Javid told reporters on Wednesday as he launched his campaign.More news: Oil steadies above $62 as OPEC cuts counter growth concerns
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Of 313 Conservative Party lawmakers, 81 have publicly backed Johnson, 32 have publicly backed Michael Gove, the environment minister, and 30 have publicly backed Hunt, The Daily Telegraph said.
The Cabinet minister was asked about the Conservative Party's handling of Islamophobia, and said he would be "very happy" for an external organisation to "take a look" to give some "external reassurance because I think we've got nothing to hide".
Labour leader Jeremy Corbyn was overheard rebuking MPs, saying that they "won't be cheering in September" as they celebrated the defeat of the motion.
Mr Johnson said: "We can not ignore the morass at Westminster where parties have entered a yellow box junction, unable to move forward or back, while around the country there is a mood of disillusion, even despair, at our ability to get things done".
Almost three years since the United Kingdom voted 52%-48% to leave the EU, the ruling Conservative Party had its worst result in centuries in a European election last month, and opinion polls indicate a snap election would produce a hung parliament.
Some of the 10 contenders, including front-runner Boris Johnson, say if they become Prime Minister, they would take Britain out of the European Union on the twice-extended withdrawal date, now set for October 31, with or without an agreement. He also raised his profile through a series of appearances on a television comedy show.
"Evidently that is not something which any of us want to do". The author has made every effort to ensure accuracy of information provided; however, neither Kitco Metals Inc. nor the author can guarantee such accuracy.