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.
Further ballots are due 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.
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Former Foreign Secretary Boris Johnson remains the clear frontrunner in the race after topping the first ballot earlier this month with 114 votes.
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”.
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”.
“What Rory has done in his campaign is to demonstrate that there are no no-go areas in this country for him or for the party which he aspires to lead”, he said.
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”.
The BBC debate – titled Our Next Prime Minister – will be hosted by BBC Newsnight presenter Emily Maitlis and broadcast on BBC One at 20:00 BST.
Candidates still in the leadership race will face questions from viewers across the country via local TV studios.
Tory leadership hopefuls to face second vote}