The Tory leadership contest will enter the next stage later when a second round of voting is held in Parliament.
Conservative MPs will vote by secret ballot in the Commons, with a result expected some time after 18:00 BST.
Any of the six remaining candidates will be eliminated from the contest if they come last or fail to secure at least 33 votes.
Those remaining in the race will take part in a live BBC debate in central London on Tuesday evening.
Remaining candidates will face further ballots later this week, where the bottom-ranked MP will be knocked out until only two candidates are left.
The final two names will then be put to a postal vote of the 160,000 Tory party members, beginning on 22 June, with the winner expected to be announced about four weeks later.
Former Foreign Secretary Boris Johnson remains the clear frontrunner in the race after topping the first ballot earlier this month with 114 votes.
Former cabinet minister Andrea Leadsom – who was knocked out of the race at the first ballot – has given Mr Johnson her support.
Speaking on LBC, she said Mr Johnson was “an election winner” who was “best placed” to take the UK out of the EU by 31 October.
Current Foreign Secretary Jeremy Hunt, who came second with 43 votes, and Environment Secretary Michael Gove, who was third with 37, should make it through to the next ballot on Wednesday if their support holds firm.
Former Brexit Secretary Dominic Raab, who received 27 votes, and Home Secretary Sajid Javid, who received 23, told reporters on Monday they were confident of making it through to the next round.
International Development Secretary Rory Stewart, who received 19 votes in the first ballot, said he had the necessary 33 backers to stay in the race “if they do what they say”.
How can you watch the debate tonight?
Our Next Prime Minister will be hosted by BBC Newsnight presenter Emily Maitlis and broadcast on BBC One at 20:00 BST.
You can also follow the debate on our live page on the BBC News website.
Alternatively, you can stream the debate online through BBC Sounds or by watching BBC One and the News Channel through iPlayer.
From 21:00 BST, the BBC News Channel will be broadcasting reaction to the debate from politicians and pundits.
The debate will be also be broadcast live on Radio 4.
Who has momentum and who is on difficult terrain?
Analysis by BBC assistant political editor Norman Smith
One candidate will definitely be knocked out of the competition, quite possibly more, because they have got to get 33 votes.
That probably puts Sajid Javid and Dominic Raab on difficult terrain.
As for Rory Stewart, the signs are that he is now beginning to build up some real momentum – not just outside Parliament but among MPs too.
He has set himself out as the soft Brexit, no no-deal candidate but also as the anti-Boris Johnson candidate.
Other contenders have started to pull their punches, looking at life beyond this contest to a Boris Johnson government. Rory Stewart is still taking punches at him.
For all those Tory MPs who want to stop Boris Johnson, he becomes a very attractive candidate.
As for Mr Johnson, tonight’s debate will be his first serious date with detail.
We will want detail on whether he is absolutely 100% going to leave the EU on 31 October or whether there is a bit of wriggle room.
Mr Stewart, who is currently sixth-placed among the remaining contenders, received a boost to his campaign on Monday evening with the endorsement of Cabinet Office Minister David Lidington.
Mr Lidington, who had backed Matt Hancock before he quit the race last week, told a rally for Mr Stewart there was a “yearning in this country for political leaders who tell it straight to people”.
Speaking on BBC Breakfast, Mr Stewart claimed the majority of Mr Hancock’s supporters were now backing him.
He added that Mr Lidington’s backing was important as it was a “vote of confidence in somebody he feels could run a cabinet and be prime minister”.
When asked on BBC Radio 4’s Today programme if he had been a spy, Mr Stewart replied: “I would definitely say I served my country. If someone asked me if I was a spy I would say no.”
Home Secretary Sajid Javid said Mr Johnson was certain to be one of the final two candidates and warned his colleagues that the race could end up looking like “a debate of the Oxford Union” – a debating society at Oxford University.
He told the Today programme he brought his own background to the job “so different and in sharp contrast to Boris”.
Speaking about his rival Mr Stewart, he said a new leader had to “properly believe in Brexit, rather than trying to reverse the decision”.
- Tory leadership: Who will be the next prime minister?
- Brexit: Where do Conservative leadership candidates stand?
Mr Johnson has agreed to take part in the BBC TV debate, after missing a debate on Sunday night hosted by Channel 4.
His low media visibility in the campaign has attracted criticism from his rivals and their supporters.
However, he picked up another cabinet endorsement on Monday, when Mr Hancock backed him as “the best candidate to unite the Conservative Party”.