The six Conservatives vying to become Britain's prime minister face off in the second round of voting on Tuesday, with the final pair to be decided by the end of the week.
The outcome of the leadership battle could determine under what conditions Britain leaves the European Union. It is currently scheduled to leave on October 31.
All of the party's 313 MPs can take part in the secret ballot in the contest to replace outgoing leader Theresa May, with further rounds scheduled to whittle the list down to a final two, who will face the party's 160,000 grassroots members.
Boris Johnson, the former foreign minister and leading Brexit campaigner, ran away with the first round of voting last week, winning the support of 114 MPs -- more than twice the number of votes won by his nearest challengers.
Johnson has said he is open to leaving the EU on October 31 without a formal deal between London and Brussels but would prefer to secure one by the deadline. Opponents of "no-deal" say it would cause economic chaos as Britain breaks up with its top trading partner.
Any candidate failing to win the support of at least 33 MPs on Tuesday will be eliminated, with the worst performing contender dropping out if they all reach the threshold.
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The result will be announced around 6pm (1700 GMT).
Two hours later, the remaining candidates will then do battle in a BBC televised debate, following a first TV showdown on Sunday that Johnson skipped. Another round of voting is scheduled for Wednesday and two more for Thursday, if required, to get the numbers down to a final two.
Then party members will pick the winner in a postal ballot with the victor set to be announced in the week starting on July 22.
Foreign Secretary Jeremy Hunt finished second in last week's vote, on 43, with environment minister Michael Gove on 37, Brexit hardliner Dominic Raab on 27, interior minister Sajid Javid on 23 and International Development Secretary Rory Stewart on 19. There are 50 votes to play for that went to four contenders who have now dropped out. Unconventional outsider Stewart has won praise for his performance in Sunday's Channel 4 debate and for his strong campaign on social media, reaching out to centre-ground voters from different parties.
Stewart told BBC Radio on Tuesday that he had "no problem" with being seen as the "stop Boris" candidate, accusing the frontrunner of making Brexit promises he couldn't keep.
In Sunday's sometimes ill-tempered Channel 4 debate, four of the five candidates said they would seek to renegotiate the draft Brexit divorce deal agreed with Brussels even though EU leaders have repeatedly ruled this out.
But Stewart said he would press ahead with the current agreement even though it has been rejected by parliament three times this year in a process that has forced Prime Minister May to call time on her leadership.
The four candidates without Stewart said they would be willing to lead Britain out of the European Union without a divorce deal on October 31 -- the current deadline set by the EU.
Johnson has also said Brexit must happen on that date, "deal or no deal". Raab, who resigned as Brexit secretary in protest at the government's compromises with Brussels, went further than the others in not ruling out suspending parliament to stop MPs from blocking a no-deal Brexit.
"I'm the only candidate committed to leaving by the end of October come what may," Raab said.
Gove, responded saying: "I will not take Britain out of the European Union against the will of parliament." Despite finishing last in the first round, Stewart has picked up support from Remain-supporting MPs, including May's deputy prime minister David Lidington, leaving Javid in a precarious position.
The interior minister took aim at rival Stewart, telling BBC Radio on Tuesday that "he is effectively telling us we should remain in the EU" and that his support was drawn from "a small constituency among my colleagues" that want to stay in the EU. Johnson has come under fire from his rivals for giving few interviews and public appearances, but will appear in Tuesday's debate.