The two contenders, Jeremy Hunt and Boris Johnson are competing for votes from party members, with the victor replacing Prime Minister Theresa May as party leader and Prime Minister of Britain's ruling Conservative Party.
Boris Johnson, the favourite to become the next prime minister, on the other hand, has refused to rule out suspending parliament to ensure Britain leaves the European Union on October 31, with or without a deal.
Jeremy Hunt has categorically stated that he would not close parliament to impose a no-deal Brexit.
On Thursday, Chief Secretary to the Treasury Liz Truss - a loyal supporter of Johnson - said prorogation should remain an option, and told Major to stop being "a back-seat driver". A legal challenge offers a potential new route. "A decision was taken just get on with it and they are not in that same polarised way that Parliament has been about this issue", she said. I think the public have got a very simple view.
The outgoing PM, who will be exiting Downing Street to make way for Hunt or Johnson by July 23, said she felt a "mixture of pride and disappointment" and that despite having to go earlier than she wanted, she had been the "right person" for the job and was "immensely proud" of what she had accomplished.
"The situation is that we are leaving by the end of October, but it would be so much better to get a deal".
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A UK Foreign Office spokesman told CNN on Saturday that whoever leaked the cables "should face the consequences of their actions". The White House responded by refusing to deal with him, and Trump branded the ambassador a "pompous fool" in a Twitter fusillade.
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Like Trump and other high-level USA officials, Ross did not specify a time frame or elaborate on what constitutes a national security threat.
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I don't believe in that. "[Motherhood] is just an addition to your life". I have bad skin days and bad hair days. "Tell me one reason!" she added.
May underscored she had done all she possibly could to try to get her Brexit deal approved and did nothing to hide her frustration with the fact that some of her most strident opponents on Brexit are those now backing Johnson. He said that while the chance of the United Kingdom leaving the European Union without an agreement "is not negligible", he still sees a negotiated exit as the "most likely outcome".
"When that has happened in the past, when Parliament has been shut down against its will, we actually had a civil war", Hunt said, referring to the 17th-century showdown between royalists and Parliament over how the country would be governed.
"I can't control what Parliament does".
"There is no conceivable justification, wherever we are, in closing down Parliament to bypass its sovereignty", Major said.
In a television showdown with his Tory leadership rival Jeremy Hunt, Mr Johnson hit out at the prospect of setting another "phoney deadline".