Conservative MPs are due to decide which two leadership candidates will go forward to a vote of party members.
Home Secretary Theresa May is the current frontrunner to replace David Cameron as PM but Justice Secretary Michael Gove and energy minister Andrea Leadsom are also in the race.
Party members will choose from the final two candidates, with the outcome due on 9 September.
But a growing group of Tory MPs are calling for the contest to be sped up.
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Former Conservative Party chairman Grant Shapps has written to MPs seeking their backing for a shortened contest, saying it was a “matter of concern for the country”. He also plans a petition.
The leadership ballot takes place between 09:00 and 16:00 BST, with the results to be announced shortly afterwards.
On Wednesday it emerged that Justice Secretary Michael Gove’s campaign manager had appealed to Mrs May’s supporters to unite in an effort to block Mrs Leadsom’s chances of getting on to the final ballot.
Nick Boles sent a text message to a number of MPs supporting Mrs May, urging them to switch sides and back Mr Gove.
He said that although he thought it “overwhelmingly likely” the home secretary would win the contest, he was “seriously frightened about the risk” of Mrs Leadsom ending up in the run-off.
“What if Theresa stumbles? Are we really confident that the membership won’t vote for a fresh face who shares their attitudes about much of modern life, like they did with IDS?” he wrote.
Mr Gove was challenged over the text at a Tory election hustings that evening, and Mr Boles later issued an apology and said Mr Gove had been unaware of the plot.
“He did not know about it let alone authorise it. And it does not reflect his views,” he tweeted.
By John Pienaar, deputy political editor
By tonight, there’ll be two contenders left.
Theresa May’s the bookies’ favourite. She’s been called a “bloody difficult woman” but also good at her job. That’s an insult she can live with, but they’ll likely get harsher.
Michael Gove’s hindered by his new-found notoriety as the best-mannered assassin at Westminster, after backing, then burying, Boris Johnson’s dreams.
Last night, it emerged Mr Gove’s campaign manager had appealed – unsubtly – to Theresa May’s supporters to unite in an effort to kill off his fellow EU Leave campaigner Andrea Leadsom’s chances. He later apologised.
Devoid of top-level political experience, she’s already having to overcome doubts about her claim to have been a financial high-flyer.
A former colleague at investment firm Invesco Perpetual, Robert Stephens, has said “she didn’t manage any teams, large or small and certainly did not manage any funds”.
That was after a friendly MP, Bernard Jenkin, spoke of her history managing “hundreds of people and billions of pounds”.
A CV listing the post Financial Institutions Director at Barclays later added the word “deputy”.
An innocent error, according to Team Leadsom – and the MP who’d boasted of her high-powered background had merely been “bigging her up”.
Maybe so, but the contest will be merciless. The fight for the top job in politics always is.
Former Tory PM Iain Duncan Smith – who is supporting Mrs May – warned colleagues against spending “the whole time stabbing each other in the back”.
At the same event, Mrs Leadsom reiterated she would not publish her tax return – unlike Mrs May and Mr Gove – unless she made the final two, saying she did not want to set a “precedent”. Both Mrs May and Mr Gove have.
But Mrs Leadsom told MPs they could come to see a summary of her tax affairs personally if they wanted to.
It comes after the leadership hopeful published details of her CV, following accusations from her opponents that she had exaggerated her previous roles in financial services.
But defence minister Penny Mordaunt, one of Mrs Leadsom’s backers, claimed there was a “concerted effort” being made to rubbish her “stellar” pre-parliamentary career.
Mrs Leadsom is due to set out her vision of the UK’s future outside the EU in a speech on Thursday morning.
Despite Mrs May’s clear lead in Tuesday’s first round vote – she got 165 votes of 329 cast – the home secretary has said she does not want the contest to be a “coronation”.
“The party and the country deserve an open, honest, robust debate – and the next leader needs to have won a mandate to lead. So there should be no deals, no tactical voting, and no coronation,” she said.
Given the margin of Mrs May’s lead, she is almost certain to feature on the two-person ballot to be put to the about 150,000 Conservative members.
The leadership contest has been sparked by David Cameron’s decision to step down as leader and prime minister after the UK voted by 52% to 48% to leave the EU.